Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

Abstract

We consider a PH/M/c queue with multiple working vacations where the customers waiting in queue for service are impatient. The working vacation policy is the one in which the servers serve at a lower rate during the vacation period rather than completely ceasing the service. Customer’s impatience is due to its arrival during the period where all the servers are in working vacations and the arriving customer has to join the queue. We formulate the system as a nonhomogeneous quasi-birth-death process and use finite truncation method to find the stationary probability vector. Various performance measures like the average number of busy servers in the system during a vacation as well as during a nonvacation period, server availability, blocking probability, and average number of lost customers are given. Numerical examples are provided to illustrate the effects of various parameters and interarrival distributions on system performance.

A Review of Vacation Queueing Models in Different Framework

“…Alfa [3] dealt with the MAP/PH/1 vacation queueing system at arbitrary times using the matrix-analytic method and obtained decomposition results for the R and G matrices. Goswami and Selvaraju [42] analyzed the non-homogeneous quasibirth-death model of a PH/M/C queue with impatient customers and multiple working vacations. They used the finite truncation method to determine the stationary distribution.…”