Performance of a Three-Queue Polling System with Probabilistic Routing

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Nigerian Association of Mathematical Physics


This research is aimed at modelling a specialized three-queue priority polling system with zero switchover times. The server dynamically allocates the system resources between two queues after serving the first queue. At near saturation levels, it is necessary to determine the performance of this routing discipline. With the assumption of poisson arrivals and exponential or Erlangian service times, the system equations were obtained via the embedded Markov chain approach. The waiting time distribution was also derived and compared with results from an appropriate simulation model. Erlangian distributed service times produced lower waiting times when compared with exponentially distributed service times for the same stream of input parameters. Hence the Erlang distribution provides a better alternative in modelling service times than the exponential distribution. This priority polling system could be deployed as a solution to certain production systems where three classes of products are produced. The polling model is also proposed as an appropriate fit for traffic systems with greedy server routing. The closed form solutions may prove to be extremely useful for system design and optimization in application areas as diverse as telecommunications, manufacturing, logistics, transportation and maintenance.



polling model, polling probability, waiting times, probability generating function, Laplace-Steiltjes transform, super cycle