The Loss Probabity Of An M/M/m Queuing System With Impatient Customers

The queuing system with impatient customers is common queuing system and has a wide range of applications in call centers, perishable goods inventory, remote communication systems and the other area. Customers will give up to leave the system when its waiting time beyond its patience time, then the loss probability exists in this system and customer loss rate is an important performance indicator. This paper studies an M/M/C queuing system with impatient customers computational formula and focuses on the calculation of the rate of customer loss. The main contents are as follows:Firstly, this paper studies the loss probability of an M/M/m queuing system with impatient customers where customers wait for service according to negative exponential distribution. The computational formula for the loss probability that proposed by Boots and Tijms does not hold for the model studied in this paper. The approximate effect of this formula on the customers’ loss probability is analyzed in this M/M/m+M queuing system.We obtain a better approximate formula through numerical experiment.After that, this paper studies the loss probability of an M/M/m queuing system with impatient customers where customers wait for service according to general distribution.The computational formula for the loss probability that proposed by Boots and Tijms does not hold for the model with the impatience of the uniform distribution, the Erlang distribution and the hyperexponential distribution through numerical analysis, and the approximate effect of this formula on the customers’ loss probability is analyzed in these three queuing systems successively. We obtain a better approximate formula through numerical experiment in the M/M/m+U system. We get a comprehensive analysis of the relation between the approximate effect of the computational formula for the loss probability that proposed by Boots and Tims and the distribution of impatient customers’ patience time in the M/M/1+M、M/M/1+U、M/M/1+kE and M/M/1+H queuing system through numerical analysis.