Asymptotic behaviour of the tandem queueing system with identical service times at both queues

O. J. Boxma, Q. Deng
2000 Mathematical Methods of Operations Research  
Consider a tandem queue consisting of two single-server queues in series, with a Poisson arrival process at the rst queue and arbitrarily distributed service times, which f o r a n y customer are identical in both queues. For this tandem queue, we relate the tail behavior of the sojourn time distribution and the workload distribution at the second queue to that of the (residual) service time distribution. As a by-result, we prove that both the sojourn time distribution and the workload
more » ... ion at the second queue are regularly varying at in nity o f i n d e x 1 ; if the service time distribution is regularly varying at in nity o f index ; ( > 1). Furthermore, in the latter case we derive a heavy-tra c limit theorem for the sojourn time S (2) at the second queue when the tra c load " 1. It states that, for a particular contraction factor ( ), the contracted sojourn time ( )S (2) converges in distribution to the limit distribution H( ) a s " 1 where H(w) = expf;w 1; g 1 + w 1; .
doi:10.1007/s186-000-8317-z fatcat:rr436ev2jvg4ncl5dohaoosroe