Consideration is given to a system of two parallel X/M/1-type queues, which share an external arrival process. The parameters of the arrival and service processes and the instantaneous cost depend on a generic 'state of environment', which changes between arrivals according to a semi-Markov (SM) process. The model is fairly versatile with respect to the arrival process, and covers SM and batch-arrival GI processes as special cases. Arriving customers are subject to admission and routing control. A suitable definition of a monotonic control policy is introduced and generalized to a standard definition that accommodates batch arrivals. For the total discounted cost criterion, the value-iteration approach is used to establish the existence of a monotonic optimal control policy for this system.<<ETX>>
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