The M/M/c/N Queuing System With The Impatient Customers And Working Vacation

As an extension of the classical vacation queue,working vacation queue system has gotten fast development.The research of working vacation queue system generalized the classical vacation queue model, it is closer to the reality, thus it has more in line with the reality application value.Impatient customers, introduced in this article, in combination with real life more service desk, the system of limited capacity situation, the working vacation queue model with impatient customers was considered.Firstly,an M/M/c/N queuing system with impatient customers and multiple working vacation was considered. By applying the Markov process theory,we establish the steady-state probability equations.Using its iterative recursive methods, we obtain the exact solutions of the steady-state probability and the main queuing performance measures.Based on these analyses,by MATLAB software,we study the effects of normal busy period service rate and the working vacation period service rate on the expected number of customers and the other queuing performance measures through numerical examples.Then, an M/M/c/N queuing system with impatient customers and asynchronous multiple working vacation was considered.Based on quasi birth and death process,the system balance equation is obtained.Based on these analyses,by MATLAB software,we study the effects of normal busy period service rate and the working vacation period service rate on the expected number of customers and the other queuing performance measures through numerical examples.