A computer system is modeled as an M/G/1 queue with an infinite buffer. Tasks arrive according to a Poisson process with

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A computer system is modeled as an M/G/1 queue with an
infinite buffer. Tasks arrive according to a Poisson process with
rate λ, and each task requires service for a duration that is given
by the random variable b, which is taken from a general
distribution, with mth moment bm and Laplace
Transform φb(s) of the pdf of b.
The state of the system at any point in time (under steady state
conditions) is the number of tasks in the system, which is given by
the random variable n, with probability generating function
Gn(z).
The computer system conserves energy by putting the CPU to sleep
when the system becomes empty, i.e., when n becomes 0. When a task
arrives, the CPU wakes up, and it takes the CPU time v, to wake up
and be ready to serve the arriving task. The random variable v has
a general distribution, with mth moment vm
and Laplace Transform φv(s) of the pdf of v.