The consequences of heavy-tailed service time distribution on a basic queuing model and its performance indicators

Abstract

Recent research showing theoretical generative models for heavy-tailed service time queues and its empirical validation implies the need for a better knowledge of the key performance indicators' behaviour under such assumption. The behaviour of the average length of the queue (Lp) and the average waiting-time (Wp)were analysed through simulation, varying system capacity, average service utilisation factor (r) and the number of servers in the systems as parameters. Comparisons were also made with service times based on Poisson processes. The results showed more sensitive variations Lq and Wq heavy-tailed service times than for Poisson-based service times. Systems having a capacity of over 1,000 entities might be considered as being systems having infinity capacity and the number of servers has a greater importance in heavy-tailed ruled processes than in Poisson processes. There was a lack adequacy Lq and Wq as key performance indicators for heavy-tailed service times, leading to unexpected and unstable results.