Abstract
In this thesis, we have studied a finite capacity M/M/R queueing system with second optional service (SOS) channel. The interarrival times of arriving customers follow an exponential distribution. The service times of the first essential service (FES) channel and the second optional service channel are assumed to follow an exponential distribution. A customer may leave the system either after the first essential service channel with probability (1−theta) or at the completion of the first essential service channel may immediately go for a second optional service channel with probability theta (0<=theta<=1). Using matrix-geometric method, we obtain the steady-state probabilities and various system performance measures. Cost model is developed to determine the optimal number of channels and the optimal system capacity, simultaneously. The minimum expected cost, the optimal number of channels, the optimal system capacity, and system performance measures are evaluated for some specified system parameters’ values. Sensitivity investigation for the expected cost with respect to specified parameters is also performed.
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