Advances, Systems and Applications
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 ℓ. |
 bℓ | Set denoting racks in PoD ℓ. |
 aℓ, e | Set denoting servers on rack e in PoD ℓ. |
 \( {\vartheta}_{n_h} \) | Data rate of VMs serving job nh. |
 Sℓ, e | Capacity of the link connecting rack e to its PoD ℓ 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 ℓ. |
 Mℓ, e | Total number of servers in rack e of PoD ℓ. |
 \( {PS}_{\ell}^{CS} \) | Static power usage rate of the CS switch in PoD ℓ. |
 \( {PS}_{\ell, e}^{ToRS} \) | Static power usage of the ToR switch on rack e in PoD ℓ. |
 \( {PD}_{\ell, e}^{ToRS} \) | Dynamic communication power usage of eth rack ToR switch of PoD ℓ. |
 \( {PD}_{\ell}^{CS} \) | Dynamic communication power usage of PoD ℓ 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 ℓ. |
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 ℓ is active and otherwise zero. |
 ξℓ | Binary variable that assumes value of one if at least one server in PoD ℓ 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 ℓ. |