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To study the optimization of a randomized control problem in an M/G/1 queue in which a removable and unreliable server may provide two phases of heterogeneous service to arriving customers.

Arriving customers follow a Poisson process and require the first essential service (FES). As soon as FES of a customer is completed, the customer may leave the system or opt for the second optional service (SOS). The service times of FES channel and SOS channel are assumed to be general distribution functions. The server requires a startup time with random length before starting service. When the server is working, he may meet unpredictable breakdowns but is immediately repaired. The inter‐breakdown time and repair time of the removable server are exponentially random variable and generally random variable, respectively. By the convex combination property and the renewal reward theorem, several system performances are obtained. A cost model is developed to search the optimal two‐threshold policy at a minimum cost. Sensitivity analysis is performed.

Expressions for various system performances are derived. Sensitivity analysis of optimal randomized control policy (based on the developed expected cost function) with respect to system parameters is investigated.

It is the first time that analytic results of sensitivity analysis of optimal randomized control policy for the complex system have been obtained which is quite useful and significant for engineers.