Performance Evaluations of Vehicle Sharing in Closed Queueing Networks System

This investigation deals with performance analysis of vehicle (taxi or motorbike or both) sharing in the structure of a closed queueing network system having M nodes and N number of vehicles. Vehicles provide service to the people who hire it at the junction (node) of the roads. Vehicles are assumed to be either in active mode or in idle mode or in vacation mode. Our main objective is to find normalizing constant by using convolution algorithm with the help of which the various performance measures-utilization of \(i^{th}\) $i^{\mathit{th}}$ vehicle consisting of N vehicles in the network, average number of vehicles at \(i^{th}\) $i^{\mathit{th}}$ node, expected total number of vehicles in the system, average time of a vehicle that it spends in waiting as well as in service in the \(i^{th}\) $i^{\mathit{th}}$ node, total waiting time of a vehicle in the queues in all the nodes, average throughput of a vehicle in \(i^{th}\) $i^{\mathit{th}}$ node in the system as well as system throughput and the probability that there are K or more vehicles in \(i^{th}\) $i^{\mathit{th}}$ node have been derived explicitly. To show real-life applications of the model the numerical results have been computed by using computer software. The model under study may attract the attention of researchers interested in the development of mathematical models of vehicle-sharing problems in the city.