Analysis of Multi-Server Queues with Station and
Server Vacations
In this paper we consider GI/M/c queues with two classes of vacation
mechanisms:
station vacation
and server vacation. In the first one the whole system, including
all the c servers, takes vacation whenever the system is empty. This
phenomenon occurs in practice, for example,
when the
system consists of a set of machines monitored by a single operator, or
the system consists of inseparable interconnected parallel machines.
While for the second class
of vacation mechanism, each server takes its own vacation whenever it completes
service and finds no customers waiting in the queue,
which occurs, for instance in the post office, when each server is a relatively
independent working unit. For both models we derive their
steady state solutions that have matrix geometric form, and
develop computational algorithms to obtain numerical solutions. We also
analyze and make comparisons of these models based on the numerical
observations.
Keywords: Queueing, embedded Markov chains,
server and station vacations,
Hessenberg matrix, matrix geometric solutions.
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