Approximate models of air transport queueing systems with partial mutual assistance between service channels

Abstract

Approximate analytical models are proposed for two types of multi-channel queuing systems with partial mutual assistance between channels and waiting in limited-size and unbounded queues. The incoming flow of requests is a superposition of several simplest flows. It is assumed that normative numbers of channels for servicing a customer that differ depending on the flow of incoming customer requests are established. In the systems of the first type the normative number of channels is not necessary: a customer is accepted for servicing if there are free channels in the system and the number of channels is smaller than the normative one. Service time is distributed exponentially with the average inversely proportional to the number of allocated channels. In systems of the second type the service of a customer is always performed by the channels of the normative number. Service time can be distributed arbitrarily (not only exponentially) with the average irrespective of the number of allocated channels. The paper presents the results of comparative analysis of the results of dealing with some tasks of designing service systems in a wide range of input data using simulation modelling and calculations based on approximate analytical models that allowed evaluating the application area of the latter and making a conclusion about their satisfactory accuracy. Examples of the use of models of technological processes of airport ground handling as queuing systems of the considered types are given.