Steady state results for the M/M(a,b)/c batch-service system (Q1072266)

The paper is concerned with a transportation system consisting of the following parts: a number of vehicles with finite capacity, a source station and destination stations described by independent, negative- exponentially distributed trip times with common mean. Passenger arrivals are Poisson. Vehicles are only dispatched when \(a\), the control limit, customers are waiting. The steady-state probabilities Pr(m vehicles idle and j customers waiting) are recursively calculated. The performance measures given in analytic form include passenger queue length distribution and mean and moments of passenger waiting time.