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Advances, Systems and Applications

Table 1 Summary of notation

From: Energy efficient temporal load aware resource allocation in cloud computing datacenters

Parameters

Definition

 R

Number of VM types.

 N

Number of jobs in the datacenter.

 K

Number of resource types.

 T

Number of different types of servers.

 Qt

Power usage of type t servers.

 \( {v}_{n_h}^r \)

Number of type r VMs required by job nh.

 \( {c}_t^k \)

Type k resource capacity of a type t server.

 \( {i}_r^k \)

Amount of type k resource required by a type r VM.

 L

Number of PoDs in the data center.

 dℓ

Number of racks in PoD â„“.

 bℓ

Set denoting racks in PoD â„“.

 aℓ, e

Set denoting servers on rack e in PoD â„“.

 \( {\vartheta}_{n_h} \)

Data rate of VMs serving job nh.

 Sℓ, e

Capacity of the link connecting rack e to its PoD â„“ CS switch.

 \( {CP}_{\ell, {\ell}^{\prime }} \)

The capacity of the link connecting CS switches of PoDs ℓ and ℓ′.

 Mt

Total number of type t servers.

 \( {M}_{\ell, e}^t \)

Number of type t servers in rack e of PoD â„“.

 Mℓ, e

Total number of servers in rack e of PoD â„“.

 \( {PS}_{\ell}^{CS} \)

Static power usage rate of the CS switch in PoD â„“.

 \( {PS}_{\ell, e}^{ToRS} \)

Static power usage of the ToR switch on rack e in PoD â„“.

 \( {PD}_{\ell, e}^{ToRS} \)

Dynamic communication power usage of eth rack ToR switch of PoD â„“.

 \( {PD}_{\ell}^{CS} \)

Dynamic communication power usage of PoD â„“ CS switch.

 PWNIC

Dynamic communication power usage of server NIC card switch (for bit per second).

 \( {P}_{m_t,{m}_{t^{\prime}}^{\prime}}^{n_h} \)

Dynamic communication power usage between two VMs serving job nh allocated in servers mt, and \( {m}_{t^{\prime}}^{\prime } \).

 \( {P^{\prime}}_{\ell, e;{\ell}^{\prime },{e}^{\prime}}^{n_h} \)

Dynamic communication power usage between two VMs serving job nh allocated in a server in rack e of PoD ℓ and in a server in rack e′ in PoD ℓ′of.

 PRℓ, e

Power supply of rack e on PoD â„“.

Variables

Definition

 \( {x}_{r,{n}_h}^{m_t} \)

Number of type r VMs in mth type t server assigned to job nh.

 \( {\overset{\sim }{x}}_{n_h}^{m_t} \)

Number of VMs in mth type t server assigned to serve job nh.

 \( {y}_{m_t} \)

Binary variable denoting on or off status of mth type t server.

 ηℓ, e

Binary variable that assumes value of one if at least one server on rack e in PoD â„“ is active and otherwise zero.

 ξℓ

Binary variable that assumes value of one if at least one server in PoD â„“ is active and otherwise zero.

 Jt

Total number of configuration patterns of a type t server.

 \( {\overset{\sim }{j}}_t \)

Configuration pattern \( {\overset{\sim }{j}}_t \) introduced by pricing problem t.

 \( {x}_{r,{n}_h}^{j_t} \)

Number of type r VMs assigned to job nh on a type t server by pattern jt.

 \( {\overset{\sim }{x}}_{n_h}^{j_t} \)

Number of VMs assigned to job nh on a type t server by pattern jt.

 \( {m}_{\ell, e}^{j_t} \)

Number of active type t servers with pattern jt in the ethrack of PoD â„“.