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Advances, Systems and Applications

Table 1 Notations

From: A cloud priority-based dynamic online double auction mechanism (PB-DODAM)

Symbols Descriptions
S Cloud service providers (sellers)
B Cloud service users (buyers)
t Time-slot
t Time (within each time-slot)
α Number of VMs (\(\alpha \in \mathbb {N}\))
θi Type of agent i
\(\hat \theta \) Collection of all agents’ types
\(\hat \theta ^{t}\) Collection of all agents’ types in time-slot t
\(\hat \theta ^{\leqslant t}\) Collection of all agents’ types from the beginning
  till the end of time-slot t
vi The single unit valuation by agent i
qi The total VMs’ quantity that agent i wants to trade
ai The agent’s arrival time
di The agent’s departure time
p Agent’s presence period in a time-slot
\(U_{i}^{\hat \theta ^{t}}\) Seller’s i utility at time-slot t
\(U_{j}^{\hat \theta ^{t}}\) Buyer’s j utility at time-slot t
P Payment rule
si,j Seller’s obtained value from the auctioneer
bi,j Buyer’s payment value to the auctioneer
Q Allocation rule
Mt Matchable pairs of asks and bids at time-slot t
\(\sigma _{i}(\hat \theta ^{t})\) Seller’s ask satisfiability in time-slot t
\(c^{p}_{i}(\hat \theta ^{t})\) Seller’s ask criticality in time-slot t and time t
\(\sigma _{j}(\hat \theta ^{t})\) Buyer’s bid satisfiability in time-slot t
\(c^{p}_{j}(\hat \theta ^{t})\) Buyer’s bid criticality in time-slot t and time t
τ Satisfiability threshold
ϕ(t) Market price
\(e^{p}_{i}(t)\) Agent i’s defer rate
ε Defer rate threshold