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

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 perfor- mance indicators’ behaviour under such assumption. The be- haviour of the average length of the queue ( qL ) and the ave- rage waiting-time ( qW ) were analysed through simulation, va- rying system capacity, average service utilisation factor ( ρ ) 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 varia- tions of qL and qW for 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 ha- ving infinity capacity and the number of servers has a greater importance in heavy-tailed ruled processes than in Poisson processes. There was a lack of adequacy of qL and qW as key performance indicators for heavy-tailed service times, lea- ding to unexpected and unstable results.