We consider a single server queue in which the customers wait for service for a fixed time and leave the system if the service has not begun within that time. The customers arrive according to a Poisson process and each arriving customer brings in a certain amount of phase-type distributed work. The service rate of a server varies according to the underlying continuous time Markov process with finite states. We construct a Markov process by using the age process and then obtain the stationary distribution of the Markov process. By using the results of the stationary distribution of the Markov process, we obtain the loss probability, the waiting time distribution and the system size distribution.
Bibliographical noteFunding Information:
We are grateful to the referees for their many valuable comments and suggestions which improved this article. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2014R1A2A2A01005831 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2014R1A1A4A01003813 ).
© 2014 Elsevier B.V.
- Impatient customer
- Loss probability
- Markov modulated service rate
- System size distribution
- Waiting time distribution
ASJC Scopus subject areas
- Modelling and Simulation
- Hardware and Architecture
- Computer Networks and Communications