Analysis of Multi-Server Queue with Self-Sustained Servers

Abstract

A novel multi-server vacation queuing model is considered. The distinguishing feature of the model, compared to the standard queues, is the self-sufficiency of servers. A server can terminate service and go on vacation independently of the system manager and the overall situation in the system. The system manager can make decisions whether to allow the server to start work after vacation completion and when to try returning some server from a vacation to process customers. The arrival flow is defined by a general batch Markov arrival process. The problem of optimal choice of the total number of servers and the thresholds defining decisions of the manager arises. To solve this problem, the behavior of the system is described by the three-dimensional Markov chain with the special block structure of the generator. Conditions for the ergodicity of this chain are derived, the problem of computation of the steady-state distribution of the chain is discussed. Expressions for the key performance indicators of the system in terms of the distribution of the chain states are derived. An illustrative numerical result is presented.

Study of markovian queueing model with F-policy, impatience customers, feedback and re-service, server vacation and breakdown

“…A multi-server vacation queueing model is analyzed by Dudin et.al. [13] where the servers are self-sustainable and can take vacation independently of system manager, by terminating the service. Other M/M/2 queueing system with vacations have been discussed in [36], [19] and [7].…”

Spatial Queues with Nearest Neighbour Shifts

“…Customers changing queues has been referred to as jockeying in the queueing theory terminology. There has been considerable work on jockeying in queues in the past [7][8][9]. The focus in these works is predominantly to analyse the steady-state distribution or find expected line-lengths or delays.…”