A multi-server queueing model with retrial connection arrivals as a model for optimisation of the traffic control

Abstract

We consider a multi-server queueing model with a finite buffer and requests arriving in connections. The number of requests in a connection is random and unknown at the connection initiation instant. Requests, which belong to the connection, arrive in accordance with a Poisson process. Admission of connections to the system is regulated by means of so-called tokens. The pool of tokens is finite. If a connection arrives and there are no tokens available, it leaves the system forever or joins the orbit and retries for access later on. The steady-state distribution of the system is analysed. The problem of the throughput maximisation under the constraint that the request loss probability does not exceed a predefined value is numerically solved. The effect of the retrial intensity, correlation and variation in the arrival process and the probability to leave the system if tokens are not available is numerically highlighted.

Keywords:

• Markovian arrival process
• asymptotically Quasi-Toeplitz Markov chains
• matrix analytic methods
• loss probability

Acknowledgements

This work was supported by the Korea Research Foundation Grant Funded by the Korean Government (MOEHRD)(KRF-2008-313-D01211).