In this paper we study a production system consisting of a group of parallel machines producing multiple job types. Each machine has its own queue and it can process a restricted set of job types only. On arrival a job joins the shortest queue among all queues capable of serving that job. Under the assumption of Poisson arrivals and identical exponential processing times we derive upper and lower bounds for the mean waiting time. These bounds are obtained from so-called flexible bound models, and they provide a powerful tool to efficiently determine the mean waiting time. The bounds are used to study how the mean waiting time depends on the amount of overlap (i.e. common job types) between the machines.
- Queueing system - Shortest queue routing - Performance analysis - Flexibility - Truncation model - Bounds
van Houtum, G-J., Adan, I. J. B. F., Wessels, J., & Zijm, W. H. M. (2001). Performance analysis of parallel identical machines with a generalized shortest queue arrival mechanism. OR Spectrum = OR Spektrum, 23(3), 411-427. https://doi.org/10.1007/PL00013360