Performance measures of parallel tandem open queueing network

The authors consider parallel four-state tandem open queueing network. The queue capacity is infinite. Passenger arrival rate is Poisson distribution and service rate is exponential distribution. The queue is constructed in the form of tandem queue, and each and every queue of tandem queue is single server (M/M/1) queue. In tandem queue, passengers will leave the system once they receive service from both the states. The purpose of this paper is to provide performance analysis for four-state tandem open queue network, and a governing equation is formulated with the help of transition diagram. Using Burke theorem, the authors formulated equation for average number of passenger in the system, average waiting time of passenger in the system, average number of passenger in the queue and average waiting time of passenger in the queue.

This paper used Burke’s theorem.

In this paper, performance analysis is done for parallel four-state tandem open queueing network and performance measure solved using Burkes theorem formula. K. Sreekanth et al. has done performance analysis for single tandem queue with three states. In this paper, the authors have done performance analysis for two tandem queues parallel with four states. This four-state tandem open queueing network is suitable for real world applications. This paper can extend for more number of service states and multi-server states according to the application, and in such case, the authors have to prove and explain with numerical examples. This analysis is more useful for the applications such as airports, railway stations, bus-stands and banks.

In this paper, parallel four-state tandem open queueing network and performance measure has been solved using Burke’s theorem formula.