The throughput rate of interchangeable parallel two-stage tandem queue with correlated service times

A parallel two-stage tandem queueing system with no intermediate waiting room is considered. An arriving customer according to a homogeneous Poisson process, when his first stage service is finished, can enter both of the second stage channels. The authors call this model an interchangeable queueing system. The service times are not independent but depend upon each other. It is assumed that their service distribution is the bivariate exponential distribution of Marshall and Olkin. The standard representation of the multivariate exponential distribution of Marshall and Olkin is derived and the throughput of this system is obtained using a matrix-geometric approach. Finally, comparison with the throughput of an ordinary parallel two-stage tandem queueing system is discussed.