MODELING OF A POLLING SYSTEM WITH VARIABLE FLOW INTENSITY

Abstract

This paper addresses the problem of simulation modeling of a stochastic polling system with a non-stationary (time-varying) arrival process. Polling systems, also known as ordered-service systems, constitute a special subclass of multi-queue queueing systems and are widely applied in telecommunications, transportation, manufacturing, inventory management, and traffic control systems. Analytical investigation of such systems becomes considerably difficult for complex configurations, which underscores the relevance of employing simulation-based approaches. A simulation model has been developed in the AnyLogic environment, incorporating three queues with distinct input flow characteristics: a heterogeneous flow following a Weibull distribution, a flow governed by an intensity schedule with daily periodicity, and a non-ordinary flow with a uniform distribution and batch arrivals. Service is provided by a single server operating under a cyclic polling order with an exhaustive discipline, whereby the server processes each queue until it is completely emptied. The service intensity is defined by a triangular distribution as a non-homogeneous Poisson process that varies over time. A comparative analysis is conducted between two models - one with variable and the other with constant service intensity. The simulation results obtained over a 700-hour period demonstrate that the model with variable intensity exhibits more stable operation: the average utilization factor is 0.81 compared to 0.88 under constant intensity, while peak loads are smoothed more effectively and the risk of queue overflow is reduced. The queue with the intensity-scheduled flow has been identified as the most heavily loaded and thus the bottleneck of the system. It is established that variable service intensity adapts more effectively to daily load cycles and provides a greater safety margin for unexpected surges in demand.