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Advances, Systems and Applications

Journal of Cloud Computing Cover Image

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.
d Number of racks in PoD .
b Set denoting racks in PoD .
a, e Set denoting servers on rack e in PoD .
\( {\vartheta}_{n_h} \) Data rate of VMs serving job nh.
S, e Capacity of the link connecting rack e to its PoD CS switch.
\( {CP}_{\ell, {\ell}^{\prime }} \) The capacity of the link connecting CS switches of PoDs and .
Mt Total number of type t servers.
\( {M}_{\ell, e}^t \) Number of type t servers in rack e of PoD .
M, e Total number of servers in rack e of PoD .
\( {PS}_{\ell}^{CS} \) Static power usage rate of the CS switch in PoD .
\( {PS}_{\ell, e}^{ToRS} \) Static power usage of the ToR switch on rack e in PoD .
\( {PD}_{\ell, e}^{ToRS} \) Dynamic communication power usage of eth rack ToR switch of PoD .
\( {PD}_{\ell}^{CS} \) Dynamic communication power usage of PoD 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 and in a server in rack e in PoD of.
PR, e Power supply of rack e on PoD .
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.
η, e Binary variable that assumes value of one if at least one server on rack e in PoD is active and otherwise zero.
ξ Binary variable that assumes value of one if at least one server in PoD 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 .