Abstract
This paper considers a FIFO single-server queue with service interruptions and multiple batch Markovian arrival streams. The server state (on and off), the type of arriving customers and their batch size are assumed to be governed by a continuous-time Markov chain with finite states. To put it more concretely, the marginal process of the server state is a phase-type alternating Markov renewal process, the marginal arrival process is a batch marked Markovian arrival process, and they may be correlated Further, service times of arriving customers are allowed to depend on both their arrival stream and the server state on arrival. For such a queue, we derive the vector joint generating function of the numbers of customers from respective arrival streams. Further assuming discrete phase-type batch size distributions, we establish a numerical algorithm to compute the joint queue length distribution at a random point in time. Finally, we show some numerical examples and examine the impact of system parameters on the queue length distribution
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of the Operations Research Society of Japan
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
