Table 1 Summary of VM provisioning concepts and their notation

A(k)

set of web applications at time k

A _i (k)

set of inactive applications at time k

A _li (k)

set of long-term inactive applications at time k

A _over (k)

set of overloaded applications at time k

S(k)

set of servers at time k

S _lu (k)

set of long-term underutilized servers at time k

S _n (k)

set of new servers at time k

S _over (k)

set of overloaded servers at time k

S _{¬o v e r} (k)

set of non-overloaded servers at time k

S _t (k)

set of servers selected for termination at time k

S _u (k)

set of underutilized servers at time k

C(a,k)

measured CPU utilization of application a at time k

C(s,k)

measured load average of server s at time k

\(\hat {C}(s,k)\)

predicted load average of server s at time k

C _w (s,k)

weighted load average of server s at time k

d e p_a p p s(s,k)

applications deployed on server s at time k

i n a c t i v e_c(a)

inactivity count of application a

M(a,k)

measured memory utilization of application a at time k

M(s,k)

measured memory utilization of server s at time k

\(\hat {M}(s,k)\)

predicted memory utilization of server s at time k

M _w (s,k)

weighted memory utilization of server s at time k

u n d e r_u_c(s)

underutilization count of server s

W(s,k)

weight of server s at time k for load balancing

A _A

aggressiveness factor for additional capacity

A _P

aggressiveness factor for VM provisioning

A _T

aggressiveness factor for VM termination

P _P (k)

proportional factor for VM provisioning

D _P (k)

derivative factor for VM provisioning

P _T (k)

proportional factor for VM termination

D _T (k)

derivative factor for VM termination

w _c

weighting coefficient for CPU load average

w _m

weighting coefficient for memory usage

w _p

weighting coefficient for VM provisioning

w _t

weighting coefficient for VM termination

C _{L A}

application CPU utilization lower threshold

C _{L S}

server load average lower threshold

C _{U A}

application CPU utilization upper threshold

C _{U S}

server load average upper threshold

I C _{T A}

inactivity count threshold for an application

I C _{T S}

inactivity count threshold for a server

M _{L A}

application memory utilization lower threshold

M _{L S}

server memory utilization lower threshold

M _{U A}

application memory utilization upper threshold

M _{U S}

server memory utilization upper threshold

W _MAX

maximum value of a server weight for load balancing

N _A (k)

number of additional servers at time k

N _B

number of servers to use as base capacity

N _P (k)

number of servers to provision at time k

N _T (k)

number of servers to terminate at time k