A NON-MARKOVIAN BATCH ARRIVAL QUEUE WITH SERVICE INTERRUPTION AND EXTENDED SERVER VACATION

Authors

Abstract

A single server provides service to all arriving customers with service
time following general distribution. After every service completion the
server has the option to leave for phase one vacation of random length
with probability p or continue to stay in the system with probability
1 􀀀 p. As soon as the completion of phase one vacation, the server
may take phase two vacation with probability q or to remain in the
system with probability 1􀀀q, after phase two vacation again the server
has the option to take phase three vacation with probability r or to
remain in the system with probability 1 􀀀 r. The vacation times are
assumed to be general. The server is interrupted at random and the
duration of attending interruption follows exponential distribution. Also
we assume, the customer whose service is interrupted goes back to the
head of the queue where the arrivals are Poisson. The time dependent
probability generating functions have been obtained in terms of their
Laplace transforms and the corresponding steady state results have been
obtained explicitly. Also the mean number of customers in the queue
and system and the waiting time in the queue and system are also
derived. Particular cases and numerical results are discussed.