We consider an infinite server resequencing queue, where arrivals are generated by jumps of a semi-Markov process and service times depend on the jumps of this process. The stationary distribution of the sojourn time, conditioned on the state of the semi-Markov process, is obtained both for the case of hyperexponential service times and for the case of a Markovian arrival process. For the general model, an accurate approximation is derived based on a discretisation of interarrival and service times.
- Semi-Markovian arrival process
- Sojourn time distribution
- Resequencing queue
Huisman, T., & Boucherie, R. J. (2002). The sojourn time distribution in an infinite server resequencing queue with dependent interarrival and service times. Journal of applied probability, 39(3), 590-603. [10.1239/jap/1034082130]. https://doi.org/10.1239/jap/1034082130