The stationary G/G/\(s\) queue
The paper deals with the Laplace-Stieltjes transform (LST) of the stationary waiting time in the G/G/\(s\) queue with FCFS discipline. (The arrival process is strictly stationary and ergodic, the service times are i.i.d. and independent of the arrival process.) First, all singularities of the LST are evaluated and constraints are derived, ensuring that the LST is holomorphic. Then, a factorization method, which is more general than the Wiener-Hopf type decomposition, is proposed. Further, an expression is given for the LST and its asymptotic behaviour for long delays. Finally, the results are applied to the GI/G/\(s\) queue (the interarrival times are additionally independent) as well as to the case of the M/G/\(s\) queue.
scientific article; zbMATH DE number 1204251