A Sequence of Two Servers with No Intermediate Queue

Customers arriving randomly are served by a queueing system consisting of a sequence of two service stations with infinite queue allowable before the first station and no queue allowable between the stations. The moment generating functions of the steady-state queueing times as well as the generating functions of the steady-state numbers of customers in the various parts of the system are obtained under assumptions of Poisson process of arrivals and arbitrarily distributed service times at both stations. The cases of regular and exponential service times are investigated in some more detail, and the results obtained are extended to include the queueing system with a sequence of two stations with a finite intermediate queue allowable between them, infinite queue allowed before the first station, Poisson process of arrivals and regular service times at both stations.