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Background/Objective: To investigate the control policy of the two-phase Mx/Ek/1 queueing system with server startup time, N-policy and unreliable server, consisting of breakdown and delay periods. Methods: Steady state equations governing the queuing system are written and is solved using the probability generating functions to obtain the steady state probabilities when the server is in different states. Results: Expected queue length when the server is in different states is derived. Also the expected waiting time in the queue is obtained through heuristic approach. Optimal threshold of N that minimizes the average cost per unit time is derived. Sensitivity analysis is performed on the optimal threshold N* based on changes in the system parameters and cost elements for the geometric arrival batch size distribution. Conclusions/Applications: This model can be obtained in the two-phase service systems like communication networks and production systems to analyze the system performance.

Optimal Control of an N-Policy Two-Phase MX/Ek/1 Queuing System with Server Startup Subject to the Server Breakdowns and Delayed Repair