Correcting a financial brokerage model for cloud computing: closing the window of opportunity for commercialisation

In April 2012, Rogers and Cliff (R&C) demonstrated a theoretical financial brokerage model for cloud computing that is profitable for the broker, offers reduced costs for cloud users, and generates more predictable demand flow for cloud providers. Relatively cheap, long-term reserved instances (RIs) are bulk-purchased by the broker, and then re-packaged and re-sold as monthly options contracts at a price lower than a user can purchase “on-demand” from the provider. Thus, the broker risks exposure on purchase for margin on sales. R&C’s result has generated significant interest in the cloud computing community and is currently the fifth most accessed research paper of all time in the Journal of Cloud Computing: Advances, Systems and Applications. Here, we perform an independent replication of R&C’s brokerage model using CReST, a discrete event simulation platform for cloud computing developed at the University of Bristol. We identify two implementation problems in R&C’s original work: firstly, the broker buys fewer RIs than the model suggests; and secondly, the broker is undercharged for RIs used. We correct R&C’s results accordingly: while broker’s profits are not as high as R&C suggest, the model still supports the theoretical possibility of a profitable brokerage. However, aggressive competition between cloud providers has reduced the cost of cloud services to users and led to the introduction of new secondary markets where users can buy and sell RIs between themselves. This has squeezed the opportunity for an intermediary brokerage. By recalibrating R&C’s model to fit current market conditions, we conclude that the commercial viability of R&C’s brokerage model has been eradicated. The window of opportunity has now closed.


Introduction
In April 2012, Rogers and Cliff (R&C) demonstrated a theoretical financial brokerage model for cloud computing that is profitable for the broker, offers reduced prices for cloud users, and generates more predictable demand flow for cloud providers [1].The broker achieves this by acting as an intermediary between cloud providers and cloud users.Firstly, the broker bulk-purchases relatively cheap, long-term 12-months or 36-months reserved instances (RIs) from the provider.Then, the broker repackages as monthly units and re-sells to cloud users at http://www.journalofcloudcomputing.com/content/3/1/2However, the cornerstone of science is the principle of replication.New findings should only be provisionally accepted-and considered with scepticism-until verified by independent replication (cf. the infamously high-profile discovery, and subsequent refutation, of neutrinos having velocity greater than the speed of light in a vacuum, e.g., [3]).Here, we perform an independent replication of R&C's brokerage model using CReST, the Cloud Research Simulation Platform (freely available for open-source download [4]).CReST was developed at the University of Bristol to address the need for a robust simulation modelling tool for research and teaching of data centre (DC) management and cloud provision; and has successfully been used to refute, revise and extend findings in the cloud computing literature [5].
Our replication study identifies two implementation problems in R&C's original work.Firstly, the broker buys fewer RIs than the model suggests; we call this the "reservations bug".Secondly, the broker underpays for RIs used; we call this the "payment bug".We demonstrate the effects of these bugs on the brokerage model and correct R&C's published results: while broker's profits are not as high as R&C suggest, the model still supports the theoretical possibility of a profitable brokerage.
However, since the publication of R&C's model, aggressive price competition between cloud infrastructure providers has dramatically reduced the cost of cloud services to end users, both from the provider directly (the primary market) and through newly introduced secondary markets where users buy and sell RIs second-hand.To reflect this, we recalibrate R&C's model using current prices charged by Amazon Web Services (AWS).Results demonstrate that competition between providers has increased market efficiency and squeezed the opportunity for a profitable intermediary brokerage.At today's prices (September, 2013), and with updated constraints to reflect the introduction of secondary markets, R&C's model is no longer theoretically profitable.We conclude that increased competition between vendors has eradicated the commercial viability of R&C's financial brokerage model for cloud computing.As such, the window of opportunity for commercial exploitation has closed.
The rest of this paper is organised as follows.In Section 'Background' we introduce R&C's brokerage model and describe our CReST implementation in Section 'Experimental method'.In Section 'Experiment 1: Model verification' we validate our model replication by generating results almost identical to those presented by R&C.The effects of the reservations bug (Section 'Experiment 2: the reservations bug') and payment bug (Section 'Experiment 3: the payment bug') identified in R&C's implementation are then demonstrated, before a set of "corrected" results for R&C's model are presented (Section 'Experiment 4: corrected replication of R&C's brokerage model').Finally, in Section 'Experiment 5: Recalibrating R&C's model to reflect current market conditions' we recalibrate R&C's model to reflect the current market for cloud provision and observe the impact this has on theoretical profits.The paper finishes in Section 'Conclusions' with our primary conclusion that R&C's brokerage model is no longer commercially viable.

Pricing the cloud
The on-demand delivery model for cloud computing resources offers a variety of benefits for business consumers: no up-front capital expenditure on (often underutilised) compute infrastructure needed to cover peak business demand; flexibility and scale-out opportunities from the ability to start and stop VM instances at will; and reduced operational costs from outsourcing maintenance and support [6].However, the on-demand model is not necessarily ideal for cloud providers, as they attempt to adhere to strict Service Level Agreements in the face of fluctuating demand.If providers could accurately forecast future resource demand, then they would have the opportunity to reduce costs by optimising electricity purchases, engineering staff, and hardware utilisation, etc. [7].At present, most providers offer a choice between an ondemand tariff ("on-demand" instances, billed per hour of usage with no upfront purchase cost [8]) and a contract tariff ("reserved" instances (RIs), leased for a fixed time period and offering significant hourly usage discounts [9]).Some providers, e.g., AWS, offer an alternative spot price tariff that varies in real-time based on current supply and demand [10].However, of these methods, only long-term RI contracts (12-months or 36-months) have the potential to aid the provider in capacity planning.
Several alternative pricing models have been proposed in academic research, most notably involving derivatives contracts, such as (European) options [11].Options contracts involve the payment of an up-front fee that gives the buyer the legal right, but not the obligation, to purchase a resource for an agreed strike-price on some later delivery date [12].These types of financial instruments are commonly used in financial markets, with underlying assets ranging from commodities such as wheat and oil, to a suite of complex financial products.In 2012, R&C demonstrated that it was possible for a cloud computing brokerage to utilise options contracts to provide cheaper resources to consumers while simultaneously aiding providers in predicting future demand [1].Significantly, R&C also demonstrated that the broker could profit from providing this service.
R&C's result has the potential to positively disrupt the delivery and pricing of cloud services.As the market in cloud resources matures and becomes more standardised, the promise of a federated cloud-where cloud users http://www.journalofcloudcomputing.com/content/3/1/2 can migrate between providers seamlessly-will enable resources to be traded as a commodity; eradicating existing concerns of vendor lock-in.In turn, this will open opportunities for brokers to enter the market, acting as intermediary market makers between users and providers.In such a scenario, R&C's result could have commercial as well as academic significance.

R&C's options model for cloud computing
Typically, the role of a broker is to facilitate the matching of supply and demand in a market.Brokerage services primarily generate profit by charging commission fees, and/or making the spread by buying at a lower price and selling at a higher price.In the cloud brokerage model of R&C [1], the broker aims to make a profit by purchasing long-term advanced obligations on resources (12-months or 36-months RIs), and repackaging them as one-month options contracts to users.
The brokerage model of R&C consists of two stages: (1) each month, the broker takes orders from clients for future resource needs by selling options, and determines how many RIs to purchase; (2) in the following month, clients can request instances from the broker by exercising their options.If the broker has capacity available from previously purchased RIs, these are sold to the users at a profit.Otherwise, the broker must purchase additional (more expensive) on-demand instances from the provider to fulfil the obligation to the client.
R&C's brokerage model extends a pricing structure that was initially developed at HP Labs by Wu, Zhang, and Huberman (WZH) [11].The WZH model financially rewards clients that reveal the true likelihood that they will utilise a resource in the future.Every month, each client, i, estimates the probability, p i , of using a resource in the following month.Clients then submit their estimation, p i , to the broker in order to purchase a resource contract.In the following month, the client is charged Used(p i ) if the resource is used and Unused(p i ) if the resource is not used, such that: and If users choose instead to purchase resources directly from the provider, they will expect to pay p i P D , where P D is the on-demand cost of a one-month instance (in WZH's model, P D = 2 [11]).It has been proven that this pricing model encourages users to truthfully submit their honest estimate of resource usage, p i , when k = 1.5 [11].
We can consider WZH's contract as an options model if the broker charges clients Unused(p i ) to purchase the option contract and then a further charge of Used(p i ) − Unused(p i ) in the following month if the option is exercised (i.e., if the resource is used).The model can then be calibrated to real-world prices by multiplying Used(p i ) and Unused(p i ) by a cost factor, C. Setting k = 1.5, to ensure truthful submission of usage probability, this gives us the final options pricing model used by R&C [1]: and where (3) is the price of an option contract, and ( 4) is the price of exercising the contract.Hence, the full cost of purchasing a one-month RI from the broker is: ( Figure 1 shows the price of options as a function of probability of usage, p i .Prices assume a cost factor of C = 1 and a monthly on-demand price of P D = 2 (as in WZH's model).We see that OptionPrice(p i ) increases non-linearly from 0 when p i = 0, to a maximum value of 0.75 when p i = 1 (blue line); and ExercisePrice(p i ) falls linearly, from a maximum value of 1.75 when p i = 0, to a minimum value of 0.25 when p i = 1 (red line).Therefore, the TotalPrice(p i ) of purchasing and exercising an option (green line) falls non-linearly from a maximum value of 1.75 when p i = 0 to a minimum value of 1 when p i = 1.As a result, the probabilistic cost of an option (p i TotalPrice(p i ) + (1 − p i ) OptionPrice(p i ); orange dots) is always lower than the probabilistic cost of purchasing an on-demand instance directly from the provider (p i .P D ; purple dots).This is the maximum constraint on the model and ensures that the user will always benefit from purchasing options from the broker, rather than buying from the provider directly.

R&C's brokerage implementation
R&C implement their brokerage framework using a simulation model consisting of: a population of user agents that have demand for cloud resources (VM instances); a cloud provider offering VM instances either on-demand or as long-term RIs; and a single broker with a market monopoly, acting as intermediary between the population of agents and the cloud service provider.We introduce each, below.

User agents
Each month, agents a i ∈ A submit their probability, p i , of demanding a resource in the following month.Agents calculate p i as the mean number of resources they have consumed during the same month in previous years.Since http://www.journalofcloudcomputing.com/content/3/1/2 each agent, a i , has a maximum demand of one resource per month, then: 0 ≤ p i ≤ 1; and the predicted demand for the full population is: ∀i p i ≤ |A|, where |A| is the size of the agent population.

Cloud provider
The cloud provider offers VM services for sale: either ondemand, at price P D per month; or reserved for R months with up front cost P Ru , plus an additional cost P Rm per month of use.Since the provider offers RIs at a discounted rate, it is always true that: However, there exists a value R < R such that: Thus, if a RI is purchased and utilised for fewer than R months, then there is no longer a cost saving; in fact, the RI will be more expensive than the on-demand price, P D .For this reason, to guarantee savings on a RI purchase, one must be certain that it will be utilised for at least R months of the full R-months term.

Broker
The broker aims to make a profit by taking the risk of purchasing long-term RIs (R = 12, or R = 36 months) from the provider and re-selling to users as one-month options contracts.Each month, users purchase options from the broker by submitting their probability of demand, p i .
The broker then uses Algorithm 1 to determine how many (additional) RIs to purchase.The broker first checks whether there is sufficient capacity available to cover the following month's demand, i.e., whether f t+1 ≥ p i .If capacity covers demand, then no further RIs are purchased; else, additional RIs are incrementally purchased until either: broker capacity covers demand (Algorithm 1, line 3); or the expected Marginal Resource Utilisation (MRU) of an additional purchase falls below a minimum threshold, θ (Algorithm 1, line 5).
Algorithm 1 Broker's algorithm used for purchasing RIs each month.The broker calculates expected MRU (Algorithm 1, line 4) by comparing historical demand, H = [h t+1−R , h t+2−R , . . ., h t ], over the previous R months, against the future resource capacity, F = [f t+1 , f t+2 , . . ., f t+R ], (the number of RIs owned) over the forthcoming R months.Using a simple forecasting mechanism that assumes future demand will equal previous demand lagged R months, the broker then calculates an expected deficit profile, D = F − H, for each forthcoming month by subtracting historical demand from future capacity, such that: Then, the expected MRU of an additional RI purchase is the proportion of months in D > 0.More formally: The MRU estimates the fraction of life (months/R) an additional reserved instance is likely to be utilised over the next R months, based on historical demand.A minimum threshold, θ, is then used to determine whether or not to make the purchase (Algorithm 1, line 5).If MRU ≥ θ then the broker buys a new RI, estimating that it will be utilised enough to make a profit.Conversely, if MRU < θ, the broker does not purchase a new RI, estimating that it will be under-utilised.For each new purchase, the broker's future capacity, F, is incremented (Algorithm 1, line 7) and the while loop restarts.However, if MRU < θ, then no more RIs are purchased and the while loop is exited (Algorithm 1, line 10).
In the following month, the broker delivers one-month instances to users that exercise their options.If the broker does not have the capacity to fulfil client demand, then additional on-demand instances are purchased directly from the provider to supply to the users.The broker is able to vary exposure to risk by altering the value of θ over the range 0 ≤ θ ≤ 1.When θ is low, the broker purchases more RIs per unit of demand than when θ is high.

Experimental method
In this section, we describe our replication of R&C's brokerage model.To ensure that the replication is entirely independent, we have implemented R&C's model on a different platform (CReST) written in a different programming language (Java).

CReST, the cloud research simulation toolkit
The Cloud Research Simulation Toolkit (CReST) was developed at the University of Bristol to address the need for a robust simulation modelling tool for research and teaching of data centre (DC) management and cloud provision.CReST is a discrete-event simulation platform written in Java, and is freely available open source under a GNU General Public License version 3.0 [4].
Although a variety of cloud simulation platforms exist (e.g., [13][14][15][16]), CReST has a unique feature set (see [5] for a detailed comparison) that enables simulation at multiple abstraction levels: from physical hardware, energy usage and thermal flows within a DC; to networked infrastructure and the virtualisation layer of application services supporting dynamic user demand.
CReST is designed as a set of coupled modules that can be independently switched on or off depending on the level of abstraction required.To ensure extensibility and module independence, CReST has a Model-View-Controller (MVC) architecture.Following Figure 2, each module has a ModuleRunner that views the time-ordered EventQueue model using Java's Observer-Observable interface.Modules observe each time-stamped Event popped from the EventQueue and decide whether to ignore the event or take appropriate action; which may include generating new Events that are subsequently pushed onto the EventQueue with a post-dated timestamp.Modules are therefore independent Observers and only interact via the EventQueue, ensuring strict delineation between modules and making it possible to switch modules on and off, delete modules, and add new modules with relative ease (for more detail on the architecture of CReST, refer to [5]).
For all experiments reported in this paper, we use CReST as the cloud simulation platform.To optimise simulation performance, we disabled several of the lowerlevel physical infrastructure modules, such as the Thermal module that tracks heat-flow in the data centre.The active modules used in all of the brokerage simulations that we perform include: Brokerage, Pricing, Events, Services and Simulation.This enables us to efficiently run experiments that simulate decades of time, without compromising on the abstraction level needed.All CReST code used to run the experiments performed here, and associated Python scripts used for data analysis and visualisation, are available to download in version 0.4.0 of CReST [4].

Parameter configuration settings
The configuration settings used for all experiments, unless otherwise stated, are detailed below: • Demand profiles: Following R&C, to simulate realistic demand for cloud resources, we consider four demand profiles generated using real demand data over the period 1988-2011 for a variety of ITrelated industries.Owen Rogers, using the UK Office for National Statistics' database of Non-Seasonally Adjusted Index of Sales, collated these data [1].Figures 3, 4, 5 and 6 displays the four demand profiles that we label using R&C's terminology: Rapid Growth (Figure 3), Steady Growth (Figure 4), Recession & Recovery (Figure 5) and Steady (Figure 6).These data were kindly supplied to us by Owen Rogers to enable us to perform a strict replication of R&C's experiments.As Rogers and Cliff explain, since historical demand data for cloud resources over long periods (necessary for the brokerage model) are not available (due to the relatively short history of cloud computing), public domain data were selected for markets that can be considered complementary to cloud computing-for example e-commerce applications, where demand for computing resources is positively related to sales executed.Furthermore, to enable the brokerage model to be evaluated across a range of market conditions, markets exhibiting qualitative variation (e.g., growth versus recession) were preferentially selected.As one may expect, all demand profiles exhibit strong seasonality, including significant spikes around Christmas.For the R&C replication experiments, we follow the same pricing scheme as [1], shown in Table 1.We take these values directly from the source code used by R&C for their brokerage model; kindly made available to us by Owen Rogers.The values in Table 1 differ slightly from those described in [1]; which states that the monthly cost of an on-demand instance is "approximately $60 for a whole month of usage" page 5, [1], and does not give absolute values for the monthly usage cost of reserved instances.In the final experiment (Section 'Experiment 5: Recalibrating R&C's model to reflect current market conditions'), we recalibrate the model using current AWS prices (September 2013) and observe the effect of these changes on the brokerage model.• Cost Factor, C: The WZH charging model [11] is based on instances with a cost of 1 or 2. The model must therefore be scaled by a cost factor, C, in order to simulate real-world pricing (refer to Equations ( 3) and ( 4)).To replicate R&C we use a cost factor of C = 35.However, in Section 'Experiment 5: Recalibrating R&C's model to reflect current market conditions', when AWS prices are updated to represent current prices, we vary the value of C to ensure the model still benefits users.• Minimum MRU threshold, θ : Following R&C, we explore a range of thresholds, θ, to determine the optimal (most profitable) value, θ opt .In each experiment, θ is varied between 0 and 1 using increments of 0.01.
In this paper, we repeat each experimental condition only once.Since the broker follows a deterministic procedure (see Algorithm 1), and since demand is fixed during each run (see Figures 3, 4, 5 and 6), there is very little stochastic variation in the model; generated only by the random ordering of user agents selected to purchase and exercise options each month.Previous studies that performed 30 repeated trials of each condition to enable statistical hypothesis testing of the results identified that 95% confidence intervals were negligible (usually narrower than the thickness of the line presented in the graph of results; see, for instance Figure two, [17]).Hence, the brokerage model of R&C is largely deterministic and we expect to replicate the results presented in [1] very closely.

Experimental results
In this section, we present a series of experimental results using our CReST replication of R&C's brokerage model.In Experiment 1 (Section 'Experiment 1: Model verification'), we present results that closely match those presented by R&C [1].However, to generate these results, it is necessary to replicate two problems identified in R&C's implementation: the reservations bug, rectified in Experiment 2 (Section 'Experiment 2: the reservations bug'); and the payment bug, rectified in Experiment 3 (Section 'Experiment 3: the payment bug').In Experiment 4 (Section 'Experiment 4: corrected replication of R&C's brokerage model'), we present a "corrected" version of R&C's results, without the reservations and payment bugs.Results are compared with those published in [1].Finally, in Experiment 5 (Section 'Experiment 5: Recalibrating R&C's model to reflect current market conditions'), we recalibrate the model using current AWS prices and updated constraints to reflect the introduction of a secondary marketplace for users to buy and sell RIs between themselves.Results demonstrate that the brokerage model is no longer profitable.one.These results offer compelling evidence that our CReST implementation is an accurate replication of R&C's brokerage implementation.However, it was not possible to achieve these results by strictly following the brokerage model.Our failure to replicate R&C's results led us to scrutinise R&C's source code, to which we were kindly given access by Owen Rogers.During this process, we noticed two inaccuracies in R&C's implementation-the reservations bug and the payment bug.Only by replicating these bugs in our CReST model were we able to produce the results (presented in Figures 7 and 8) that closely match those of R&C.This verifies that the reservation and payment bugs were present in R&C's model implementation and that the headline results presented by R&C are inaccurate.Given the significant interest that R&C's results have generated within the cloud computing community, this is an important discovery.In the following sections, we demonstrate the impact that the reservations and payment bugs have on R&C's results.

Experiment 2: the reservations bug
In R&C's implementation of the brokerage model, there is a bug in the software code that causes the broker to purchase fewer reservations than the model suggests.This occurs during the while loop in the PurchaseReservedInstances function detailed in Algorithm 1 (see Section 'Broker').Each time the broker decides to purchase a new reserved instance, i.e., when "if MRU ≥ θ" is True (line 5), the broker then allocates this new purchase to the next unit of demand.In essence, there is an additional line in Algorithm 1, between lines 8 and 9, which reads: This is the reservations bug-each new RI purchase is effectively allocated to two units of demand.As a result, the broker purchases fewer RIs than the brokerage model dictates.(For further discussion of the reservations bug, refer to pp. 26-33, [18]).
We can see the effect of removing the reservations bug from our CReST implementation in Figures 9 and 10.For 12-months RIs, the effect is most clear (Figure 9).We see that for all markets, the total profit for brokers is much lower when θ < 0.5.In particular, in the Recession & Recovery market, when θ = 0, broker's profits are 70% lower than R&C report on 12-months RIs.A similar, but smaller effect is also observed for 36-months RIs (Figure 10).
This result can be explained as follows.As the value of θ falls, the statement "if MRU≥ θ" (line 5) is more likely to evaluate True.Therefore, smaller values of θ are more affected by the reservations bug than larger values of θ.When the reservations bug is not present, the broker purchases more RIs per unit of expected demand.However, since under-utilised RIs reduce the broker's profits (and potentially generate a loss), we see profits most affected when θ is small (i.e., when the broker takes on most risk from purchasing RIs).
We thus conclude that the reservations bug has artificially inflated the brokerage profits presented by R&C.This effect increases as the value of θ falls and is greatest when θ < 0.5.

Experiment 3: the payment bug
Algorithm 2 describes the process used to calculate the monthly usage fees a broker must pay to satisfy user Figure 10 No reservations bug.Total profits plotted against θ using 36-months reserved instances (compare Figure 8).http://www.journalofcloudcomputing.com/content/3/1/2 demand.Each month, the number of options exercised by users is the demand that the broker must satisfy.The broker compares demand against the number of RIs owned-the current capacity (Algorithm 2, line 3).If capacity covers demand, then the broker simply pays the provider the monthly fee to utilise enough RIs to fulfil demand (Algorithm 2, line 4).Else, if capacity is less than demand, the broker first pays to utilise all RIs owned (Algorithm 2, line 6), before covering excess demand by purchasing additional on-demand instances from the provider (Algorithm 2, lines 7-8).

Algorithm 2
The payment bug-line 6 is missing from R&C's implementation.return fees 11: end function From an inspection of R&C's code, it is apparent that R&C have erroneously implemented the procedure described in Algorithm 2 to calculate monthly utilisation fees that the broker must pay the provider.In particular, R&C's code has accidentally omitted line 6.This is the payment bug-during months that demand is greater than capacity, the broker does not pay the monthly utilisation charge for RIs.Although the payment bug only manifests when there is excess demand for broker resources (and hence is more likely to occur when θ has a high value), it has a significant effect on results.(For further discussion of the payment bug, refer to [18]).
Figures 11 and 12 present results from our CReST replication of R&C's model with the payment bug corrected (to ensure a controlled comparison, the reservations bug remains).We see that the broker's profits are much lower across all thresholds, θ, and in all markets.Comparing Figure 11 with Figure 7, we see that, for 12-months RIs, maximum profits (θ = θ opt ) fall by more than 50% in all markets (and more than 75% in the Steady market).Likewise, comparing Figure 12 with Figure 8, we see that, for 36-months RIs, maximum profits fall by more than 33% in all markets (and more than 50% in the Steady market).Clearly, the payment bug is responsible for a large inflation in the brokerage profits reported by R&C.

Experiment 4: corrected replication of R&C's brokerage model
Here, we perform a fully "corrected" replication of R&C's model with both bugs removed.Figures 13 and 14 once again show total profits against θ.It can be seen that total profits are significantly lower than those presented by R&C.However, the broker remains profitable under all conditions other than when investing in 12-months RIs in a Recession & Recovery market using a low MRU threshold, θ ≤ 0.07.Under these conditions, the broker invests too much capital in purchasing RIs that are then under-utilised by users.
Table 2 presents a summary of results.This table is intended to replace the results table presented by R&C Table one, [1].In general, the results in Table 2 largely support the conclusions drawn by R&C.Apart from the particular loss-making conditions described above, the broker profits under all other conditions and will increase profits: by considering past performance (i.e., by selecting a value of θ > 0); and by investing in 36-months RIs rather than 12-months RIs.Therefore, although the reservations and payment bugs have a significant impact on absolute profits (the corrected model produces between 31% and 68% less maximum profit than the original model; see Table 3), the headline results presented by R&C largely hold true in the corrected model.
However, in the following section, we recalibrate R&C's brokerage model using current market conditions (September 2013) to test whether the conclusions are still valid.

Experiment 5: Recalibrating R&C's model to reflect current market conditions
Since the publication of R&C's brokerage model in April 2012 [1], the market for cloud computing provision has become increasingly competitive.Over the last 18 months, AWS' prices have fallen rapidly (compare Table 4 with Table 1); and new RI price tiers have been introduced ("Light", "Medium" and "Heavy" Utilisation), enabling users more flexibility to offset upfront payment, P Ru , against the monthly utilisation rate, P Rm .
Perhaps more significantly, AWS have also introduced a secondary marketplace venue for cloud users to buy and sell RIs-the Amazon EC2 Reserved Instance Marketplace (ARIM) [19,20].ARIM enables cloud users that own RIs to re-sell the time remaining (in whole months).For instance, if a user with 9 months and 2 weeks remaining on a 12-months RI decides that the RI is surplus to requirements, the instance can be resold on ARIM with a reservation period of 9 months.Sellers are able to offer Figure 11 No payment bug.Total profits plotted against θ using 12-months reserved instances (compare Figure 7).For values of θ ≤ 0.4, profits are similar (non-identical) for all markets.This is purely co-incidental.
their RIs for sale at any price, P A , but are encouraged by default to use a "linear price drop", such that: where r is the time in whole months remaining on the instance, R is the RI's full term (in months), and P Ru is the price of the instance when bought directly from the provider [19].
ARIM has the potential to radically disrupt the market for RIs.Firstly, the introduction of a re-sale venue means that investment in RI purchases on the primary marketi.e., directly from the provider-are less risky, as unwanted time can be traded away.Secondly, the availability of RIs on the secondary market with contract periods shorter than those available on the primary market (since r ≤ R) produces a further reduction in the purchase risk of RIs.Thus, by enabling the trade of risk, ARIM encourages users to switch from the (more expensive, but less risky) Figure 12 No payment bug.Total profits plotted against θ using 36-months reserved instances (compare Figure 8).http://www.journalofcloudcomputing.com/content/3/1/2 Figure 13 Corrected model.Total profits plotted against θ using 12-months reserved instances (compare Figure 7).
on-demand purchase model, to the RI purchase model.This benefits AWS, as an increase in the sale of RIs on the primary market generates more predictability (in revenue and demand) for the provider and encourages user loyalty.
In light of these changes, it is necessary to recalibrate the brokerage model of R&C and address assumptions of the model that may no longer hold.

Current AWS pricing (September 2013)
Table 4 presents current AWS prices for a Medium Utilisation RI (prices assume 730.5 hours/month; 365.25 days/year).The new tiered pricing of RIs by AWS means that users can select to purchase RIs based on their likely utilisation.Higher utilisation RIs have a higher up-front cost, P Ru , and lower usage cost, P Rm , than lower utilisation RIs.Here, we select Medium Utilisation RIs as a simple proxy for average prices, however, the conclusions drawn are largely unaffected by this choice.We can see from Table 4 that all prices have fallen roughly 30% since April 2012 (compare Table 1).In this section, we use these new AWS prices to test the profitability of the brokerage model in the current market.However, when calibrating Figure 14 Corrected model.Total profits plotted against θ using 36-months reserved instances (compare Figure 8).http://www.journalofcloudcomputing.com/content/3/1/2 the model with real-world prices, it is necessary to adjust the cost factor, C, to ensure that the options prices that the broker offers remain low enough to benefit users (and hence ensure that each user, i, estimates their probability of exercising an option, p i , truthfully).In the following section we describe how we derive C, given the current market landscape.

Cost factor
The pricing structure of the brokerage model is defined as: where TotalPrice(p i ) and OptionPrice(p i ) are given by equations ( 5) and (3), respectively.For the model to offer value to users (a requirement necessary to remain within the WZH bounds for truth-telling conditions [11]), ModelPrice(p i ) must be lower than (is bounded by) the lowest available price on the market, P M , such that: Then, C max is the value of C that maximises broker's profits, i.e., the highest value of C that satisfies inequality (12).
In [1], R&C assume that P M is the price of an on-demand instance purchased directly from the provider, P D .Using current AWS prices (Table 4), we have: When using R&C bounds, the maximum cost factor C max = 25 (see Figure 15; where the blue-dashed line is the upper-bounds on the model, p i P D , and the solid blue line represents ModelPrice(p i ) when C = 25).Thus, when C = 25, the user is incentivised to purchase options rather than purchasing on-demand.
However, since the publication of [1], the introduction of ARIM means that users can now purchase instances on the secondary market (at price P S ).We can be sure that one month RIs offered for sale on ARIM will have price P S < P D , since RIs inherently offer less flexibility than on-demand instances.Therefore, the assumption that P D is the best available price is no longer reasonable-we must now consider P S as the best available price.
We can estimate the likely value of P S using simple game-theoretic reasoning.Sellers on ARIM want to maximise price subject to the constraint P S < P D .However, sellers must offer a competitive price to ensure a sale.If P S > P C , where P C is the cost price of a RI to the seller, then there exists an opportunity for a professional re-seller to enter the market at price P B and profit from simply buying long-term RIs from the provider, slicing into monthly units, and re-selling at a price P C < P B < P S .In the limit, therefore, we expect ARIM to tend to an equilibrium price such that: lim t→∞ P S = P C .At prices P S < P C , the seller makes a loss on each sale.This is clearly not a profitable strategy to pursue, and hence professional re-sellers on ARIM will not price at these values.However, there may be individual firms that attempt to dump surplus RI volume at a price P S < P C to ensure a sale.But, assuming that ARIM is a liquid market-i.e., demand on ARIM is high enough to ensure that a competitive sale price will always result in a sale-then there is no need for a seller to  reduce prices below P C unless the volume to be sold forms a significantly large proportion of the market (at which point there will be an adverse "price impact", such that P S must be lowered in order to discover enough demand to fulfil the volume [21]).For simplicity, we assume that ARIM is a liquid market and ignore commission costs (ARIM charges a 12% commission fee on all sales [19]).Then, we expect: We consider P S to be the new strong bounds on the brokerage model (see Figure 15, green dashed line).When C max = 10, broker's profits are maximised (Figure 15, green solid line), while ensuring that users are incentivised to purchase options from the broker rather than purchase RIs on ARIM.
Finally, we also consider a weak bounds on the model, such that P M = P W , where: P W assumes that RIs are available to users on ARIM only half of the time.We introduce this as an approximation of ARIM being an illiquid market, such that supply cannot always cover demand.Hence, under these conditions, users cannot always be certain that a RI will be available for purchase on ARIM.Under this condition, C max = 18 (Figure 15, red line).
Although we expect the strong bounds to be a more realistic expectation of the long-term equilibrium price on ARIM, we include the weak bounds as a transitional model of ARIM, since it is likely to take some time before ARIM gains enough traction to become a liquid market trading at equilibrium.

Empirical evidence of instance prices from ARIM data
At the time of writing (March 2014), ARIM has been operational for 18 months.However, since Amazon AWS do not currently publish historical ARIM trade data it is impossible to perform a full analysis of the behaviour of the market.Therefore, to determine the level of RI prices available on ARIM, a snapshot of current price data was collected across all instance types and all availability zones in US-East on 14th March 2014, 13:14 GMT.To normalise the data across instance types, the effective hourly rate (EHR) for each instance, defined as: Effective hourly rate (EHR) = upfront cost term in hours + hourly rate, (16) was indexed against the effective hourly rate of the original full-term instance when purchased from AWS, such that: Therefore, when EHR index = 1, the ARIM list price has the same effective hourly rate as the same instance purchased directly from the provider-this is also equivalent to the linear drop price of the instance, defined by equation (10).Index values below 1 indicate that ARIM prices are effectively lower than provider prices, and values above 1 are effectively higher than provider prices.
Figure 16 represents a snapshot of all EHR index prices across all instance types against the proportion of time remaining on the RI term.Each bubble plots an individual quote price, with bubble area proportional to volume (number of instances) listed at that price.It can clearly be seen that the majority of instances are quoted for sale at, or just below, EHR index = 1.Therefore, the argument presented previously in Section 'Cost factor'-that prices on ARIM are likely to be available at the linear drop priceappears valid.This supports the strong assumption, P S (14), which implies a cost factor C max = 10.
However, a recent blog article presents analysis concerning the liquidity of ARIM [22].The author monitors ARIM over a 45-day period between 28th November 2013 and 9th January 2014, taking hourly snapshots of the marketplace.After cleaning the data, the author uses survival function estimates to calculate that the median time-tosell (for instances that eventually do sell) is 15.5 days and the censoring ratio is 30% (the proportion of instances unsold at the end of the observed interval) [22].This analysis suggests that ARIM is still an illiquid and fragmented market, thus supporting the weak assumption, P W (15), which implies a cost factor C max = 18.
The empirical evidence presented here supports the argument proposed in Section 'Cost factor'.Specifically, while the strong bounds offer a more realistic expectation of the long-term equilibrium of ARIM, the weak bounds are likely to be a more accurate transitional model of the market's current illiquidity.This argument is further supported by evidence generated from a multi-agent simulation of ARIM [23], using a simple model containing a population of ZIP trading agents buying and selling RIs on a simulated exchange (see [24] for ZIP's design and [25][26][27] for a review of ZIP).Results from the model showed that simulated trade prices tend to equilibrate at the linear drop price when the market is liquid; and equilibrate below the level required for a broker to profit when there is an excess of sellers dumping unwanted capacity into the market [23].

Results
When running the brokerage model using current AWS prices (Table 4) and a cost factor C = 25, the brokerage model remains profitable (at a level similar to that  presented in Figures 13 and 14).However, C = 25 is only acceptable if we assume R&C's upper bounds (Figure 15).Given the introduction of ARIM, we reject this result and re-test the brokerage model using cost factors of C = 18 (weak assumption) and C = 10 (strong assumption).
Figure 17 shows total broker profits for 12-months RIs when C = 18.For all market conditions, the broker makes a loss.This demonstrates that, under the weak assumption, the brokerage model is no longer profitable for 12-months RIs.However, the model does remain profitable for 36-months RIs, but at a much reduced rate (maximum profit is less than $0.4M).Hence, as ARIM grows in popularity and becomes more liquid, we will expect the brokerage model to be much less profitable.
Finally, when running the model using C = 10, 36months RIs are no longer profitable (see Figure 18).Thus, under the strong assumption, the brokerage model is no longer profitable under any condition.This effectively Figure 18 September 2013 calibration (C=10).Total profits plotted against θ using 36-months reserved instances.http://www.journalofcloudcomputing.com/content/3/1/2 demonstrates that, once ARIM matures into a liquid market, there will be no profit available for a broker using R&C's model.Thus, we conclude that (if it hasn't already) the window of opportunity to commercially exploit the brokerage model of R&C will soon close.

Discussion: the effect of broker competition
Throughout this paper, and following directly from R&C's brokerage model, it has been assumed that the broker has a monopoly position.Indeed, the WZH reservation model, which R&C's brokerage model extends, is described by the authors as a mechanism that "extracts revenue similar to that of a monopoly provider practicing temporal pricing discrimination with a user population whose preference distribution is known in advance" [11]).Thus, the brokerage model relies on the broker being somehow able to position itself as a monopoly provider of options; perhaps through an exclusive licensing agreement with the provider.
We have demonstrated in Section 'Results' that R&C's corrected brokerage model is profitable under current AWS prices when acting as a monopoly provider of options.However, we have also shown that this profit is eroded through the availability of cheaper instance prices on ARIM.What we have not considered is the impact that competition between multiple brokers may have on profit.
It has been shown that when competition is introduced into a market dominated by a monopolistic supplier performing differential pricing-similar to R&C's brokerage model-there will be an increase in intra-firm price dispersion [28].That is, the difference between the highest and lowest prices charged by each individual firm will increase: "as the market becomes more competitive, prices become more dispersed, a pattern documented in the airline industry" [28].In the airline industry for example, one can observe that while competition between airlines has lowered the price of the cheapest economy seats (booked off-season, non-refundable, non-transferable, booked in advance), the most expensive seats (first or business class, flexible dates, refundable) have experienced rapid price inflation.
Therefore, in a market containing multiple brokers using R&C's brokerage model we would expect competition between brokers to similarly increase intra-firm price dispersion.Therefore, either: (i) the minimum price (when the probability of an individual consumer exercising the option p i = 1) will fall; or (ii) the maximum price (p i = 0) will rise; or (iii) both the minimum price will fall and the maximum price will rise together.However, since the maximum price is constrained by the cost factor, C, it is impossible for the maximum price to increase beyond the bounds determined by C max (otherwise the brokerage model will no longer encourage consumers to act truthfully, thus destroying the model).Hence, for competition to occur, either the minimum price (p i = 1) must fall, or the cost factor must fall.Either way, since the maximum price (p i = 0) cannot simultaneously rise, then the brokers' margins (and ultimately, the brokers' profits) must fall.In reality, the dynamics of a competitive brokerage market, resulting from the coevolutionary interaction of multiple adapting entities, are likely to be complex (see, for example [29,30]).However, we fundamentally expect a downward trend in brokerage profits over the long-term.
In summary, therefore, we reach the intuitive conclusion that competition between brokers will reduce brokers' profits.Furthermore, this effect will be exacerbated by the availability of "cheap" instances on the secondary market, ARIM.Thus, unless the cloud provider acts as a monopoly brokerage supplying instance options, R&C's brokerage model looks unsustainable in the face of potential competition.That is not to say that profitable opportunities do not exist via alternative differential pricing models using temporal demand forecasts (for example [31,32]), or alternative cloud brokerage models.

Conclusions
The financial brokerage model for cloud computing presented by Rogers & Cliff (R&C) demonstrated that there is an opportunity to profit from acting as an intermediary between cloud providers and cloud users.This result has received significant attention within the cloud computing community and the publication is currently the fifth most accessed article of all time in the Journal of Cloud Computing: Advances, Systems and Applications [2].
Here, we have presented results from our independent replication of R&C's brokerage model using CReST, the Cloud Research Simulation Toolkit.In doing so, we have identified two problems with R&C's implementation: the reservations bug, which forces the broker to be more riskaverse than the brokerage model suggests; and the more influential payment bug, which incorrectly calculates the payment a broker makes to the provider, thereby inflating the broker's profits.
After demonstrating the impact of the reservations and payment bugs, we then presented a set of "corrected" results for the brokerage model, intended to replace those presented by R&C.While the corrected results demonstrate that the brokerage model is less profitable in absolute terms than previously thought, the conclusions drawn by R&C still largely hold.
However, since R&C's model was published, the landscape for cloud computing provision has radically altered.In particular, increased competition between providers has driven down prices and encouraged innovation, such as the introduction of a secondary marketplace-Amazon's Reserved Instance Marketplace (ARIM)-for users to buy and sell reserved instances.To reflect these http://www.journalofcloudcomputing.com/content/3/1/2 changes, we updated the assumptions of R&C's model, by altering the maximum allowable cost factor.
In R&C's original work, the model was bounded to ensure that options from the broker are always cheaper for users than an on-demand instance purchased directly from the provider.However, the introduction of ARIM means that users can now purchase instances on the secondary market for prices cheaper than the on-demand price.Therefore, we assume that the price of an option must always be cheaper than the expected price of a reserved instance on ARIM.Under this assumption, we show that the broker's profits will reduce as ARIM grows in popularity and at the expected equilibrium the brokerage model is no longer profitable.
We therefore conclude that the introduction of a new secondary market venue for users to buy and sell RIs has closed the window of opportunity to commercially exploit the brokerage model of R&C.This is particularly compelling, since R&C's brokerage model assumes that the broker has a monopoly position.Indeed, the WZH reservation model, which R&C's brokerage model extends, described by the authors as a mechanism that "extracts revenue similar to that of a monopoly provider practicing temporal pricing discrimination with a user population whose preference distribution is known in advance" [11]).Thus, the brokerage model relies on the broker being somehow able to position itself as a monopoly provider of options; perhaps through an exclusive licensing agreement with the provider.However, every user now has the ability to trade RIs on ARIM.Thus, the assumption that the broker has a monopoly position is no longer tenable.For this reason, the brokerage model must be able to compete with prices expected on the secondary market.As we have shown, this is not possible.

Figure 1
Figure 1 Option prices.With a cost factor C = 1 and on-demand price P D = 2, the cost of options from the broker (orange dotted line) is always cheaper than purchasing an on-demand instance directly from the provider (purple dotted line).

Figure 2
Figure 2 MVC architecture of CReST.Each module has a ConcreteModuleRunner object that extends the AbstractModuleRunner class.The AbstractModuleRunner implements the Observer interface and uses the method Observer.update()to view each new timestamped Event popped from the time-sorted EventQueue.The ConcreteModuleRunner then chooses to ignore or react to the Event, which may cause future Events to be generated and added to the EventQueue.

•
Running time: Each simulation lasts 276 simulated months.This time period is determined by the available demand data utilised by R&C (refer to Figures 3, 4, 5 and 6).Results statistics are all calculated up to and including 2010.• Number of user agents: Following R&C, we set the number of user agents in the population to |A| = 1000.• RI Period and learning period length: Following R&C, we explore RIs with both R = 12 and R = 36 months.At the start of each simulation, there is a learning period of R months such that the broker observes the market and updates historical demand, but does not trade.• Pricing: Prices for cloud computing resources in the real world continue to fall as providers face increasing competition.

Experiment 1 :
Model verificationHere, we present results that closely replicate those presented by R&C[1].Figures7 and 8show total broker profits as a function of θ for 12-months and 36-months RIs, respectively.These graphs are directly comparable to Figuresix,[1] for 12-months RIs and[1], Figure seven for 36-months RIs.To the naked eye, these results are qualitatively identical to those presented by R&C; and also quantitatively very similar, with broker profits across all markets falling within 2% (the majority within 1%) of R&C's published values[1], Table

else 6 :
fees ← capacity × P Rm pay monthly fee for reserved instances used 7: excessDemand ← demand − capacity 8: fees ← fees + excessDemand × P D purchase on-demand instances to cover excess 9:

Figure 15
Figure 15 Cost factor bounds.Maximum cost factor, C, given upper bounds on options pricing.

Figure 16
Figure 16 Snapshot of US-East ARIM quote prices for all instance types, 14th March 2014 13:14 GMT, with bubble area proportional to liquidity (volume) at a specific price.An effective hourly rate index of 1 indicates that an instance is listed at the linear drop price.Values below (above) 1 indicate instance is listed at a price below (above) the linear drop price.Clearly, the majority of instances are listed at or below the linear drop price (index ≤ 1).

Table 1 Instance prices
AWS prices used for R&C replication studies (AWS prices in June 2011).