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.
Highlights
In communication networks, multiple servers are used to reduce the traffic congestion and improve the system performance
To understand the network behavior and to make intelligent decisions in their management, these systems can be modelled as multiserver queueing systems with server vacations
Stationary distribution of a multiserver vacation queue with constant impatient times is studied by Sakuma and Inoie [16]
Summary
Multiple servers are used to reduce the traffic congestion and improve the system performance. Stationary distribution of a multiserver vacation queue with constant impatient times is studied by Sakuma and Inoie [16]. Baba [28] considered the GI/M/1/WV system with general independent arrival process where the distributions of the vacation duration times and service times are exponential. A connection is terminated by pressing the stop button, refreshing the connection, or following a different link This behavior can be termed the impatience of a user in LANs. To study the effect of multiple servers and user impatience on the performance in a WDM network, we consider in this paper a multiserver model with asynchronous multiple working vacation (AMWV) policy and impatient customers. Lin and Ke [31] presented a multiserver WV queue with exponential interarrivals but none of these models represent systems with nonexponential arrivals or state-dependent systems.
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