Steady state analysis of M/M/1 Queue with Two-Phase, Server Time-Out and Breakdowns

Abstract

This paper analyzes M/M/1 vacation two-phase queueing model with server Start-up, Time-out and Breakdowns. Customers arrivals are assumed as Poisson process and be given batch mode in the first phase followed by individual models second phase. Arrivals during batch service are allowed to enter the batch without Gating. After providing the second phase of service to all customers individually, server returns to first phase to serve the existing customers followed by individual service. If no one presents, then server waits for a fixed time ‘C’ is called server Time-out. If units arrived during this fixed time, then the server starts the cycle again by providing them batch service followed by individual service, otherwise after expiration of fixed time he takes a vacation. The server comes back from vacation, after N-customers are accumulated. The server passes a random period as pre-service procedure after coming back from vacation. During individual service the server is susceptible to random failures. Various performance measures are evaluated in steady state. Cost function is established to define the threshold and sensitivity analysis is also presented through numerical examples.