Priority Queueing System With Impatient Customers

Customers’ service with priority is a common phenomenon in the queue system. At thesame time, it usually accompanies balking and reneging, that is the arriving customersmay not enter the system or they may leave the system without service because ofimpatience, these customers are called impatient customers. The priority queueing systemwith impatient customers has wide applications in the special customers of servicemechanism, the perishable goods of sales strategy, communication system and signaltransmission of broadband network and other fields. Therefore, it has important theoreticalsignificance and application value for studying a priority queueing system with impatientcustomers.In this paper, we considered a single-server queueing system with balking, renegingand priority, a multi-server priority queueing system with balking, reneging and priority,and a priority queueing system with reneging and multiple vacations, respectively.Firstly, the single server queueing system with balking, reneging and priority isconsidered. By using the block matrix solution method, we derive the steady-stateprobability distribution of the two-class customers. Besides, we obtain some performancemeasures of the system such as the mean queue length, the average rate of the customerreneging and so on. We also make some numerical analysis, focusing on analysis andcomparation of the class-2customers’ performance measures under different balking ratefunction.Secondly, we analyze a priority queue with reneging and multiple vacations. By usingthe quasi-birth-and-death process and matrix solution method, we get iterative calculationformula of the steady-state probability vectors, and then we obtain some performancemeasures of the system. Finally, we make numerical verification of the results and analyzethe effect of vacation rate on the performance measures.Finally, we study a multi-server queue with balking, reneging and priority. Accordingto Markov-process theory and matrix solution method, we get iterative calculation formulaof the steady-state probability vectors. Besides, we deduce some performance measures ofthe system such as the mean queue length, the average rate of the customer reneging and so on. Finally, we make some numerical analysis, focusing on analysis of the effect ofparameter change on the mean queue length of the class-2customers.