Research on M/M/1 Queue of Exponential Departure Intensity

Abstract

For the queuing model with a single service window in system, the length of a queue has a great influence on the service rate. Study on the M/M/1 queuing model with variable service has practical significance. Also, the study can provide the basis for improving both economic efficiency and service efficiency. So far, there is little discussion about the departure intensity of exponential form for M/M/1 queue. On the basis of the study of Singh and Kumar Acharya (2021), this thesis has established the M/M/1 impatient waiting queue of leaving intensity of ${\alpha }_k=k{e}^k$ . First, the systems’ condition shift chart of the waiting queue has been drawn. Then, we obtained the steady-state distribution and analyzed the system performance measure. We gave an example to show the application of the model finally.