Services within a busy period of an M/M/1 queue and Dyck paths

Details Services within a busy period of an M/M/1 queue and Dyck paths Services within a busy period of an M/M/1 queue and Dyck paths

2007-07-27

arxiv.org/abs/0707.4124v1

Queueing Systems / Queueing Systems Theory Appl 49, 1 (2005) 73-84

Computer Science

Discrete Mathematics

Scientific paper

10.1007/s11134-004-5556-6

We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the beginning, at the end, or in the middle of the busy period. It enables as a by-product to prove that the process of instants of beginning of services is not Poisson. We then proceed to a more precise analysis. We consider a family of polynomial generating series associated with Dyck paths of length 2n and we show that they provide the correlation function of the successive services in a busy period with (n+1) customers.

Affiliated with

Also associated with

No associations

Rating

Services within a busy period of an M/M/1 queue and Dyck paths does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Services within a busy period of an M/M/1 queue and Dyck paths, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Services within a busy period of an M/M/1 queue and Dyck paths will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-271899