Optimal control of M/M/1 two-phase queueing system with state-dependent arrival rate, server breakdowns, delayed repair, and N-policy

Abstract

In this paper, we examine a two-stage queueing system where the arrivals are Poisson with rate depends on the condition of the server to be specific: vacation, pre-service, operational or breakdown state. The service station is liable to breakdowns and deferral in repair because of non-accessibility of the repair facility. The service is in two basic stages, the first being bulk service to every one of the customers holding up on the line and the second stage is individual to each of them. The server works under N-policy. The server needs preliminary time (startup time) to begin batch service after a vacation period. Startup times, uninterrupted service times, the length of each vacation period, delay times and service times follows an exponential distribution. The closed form of expressions for the mean system size at different conditions of the server is determined. Numerical investigations are directed to concentrate the impact of the system parameters on the ideal limit N and the minimum base expected unit cost.