368 research outputs found
Analysis of Multiserver Retrial Queueing System: A Martingale Approach and an Algorithm of Solution
The paper studies a multiserver retrial queueing system with servers.
Arrival process is a point process with strictly stationary and ergodic
increments. A customer arriving to the system occupies one of the free servers.
If upon arrival all servers are busy, then the customer goes to the secondary
queue, orbit, and after some random time retries more and more to occupy a
server. A service time of each customer is exponentially distributed random
variable with parameter . A time between retrials is exponentially
distributed with parameter for each customer. Using a martingale
approach the paper provides an analysis of this system. The paper establishes
the stability condition and studies a behavior of the limiting queue-length
distributions as increases to infinity. As , the paper
also proves the convergence of appropriate queue-length distributions to those
of the associated `usual' multiserver queueing system without retrials. An
algorithm for numerical solution of the equations, associated with the limiting
queue-length distribution of retrial systems, is provided.Comment: To appear in "Annals of Operations Research" 141 (2006) 19-52.
Replacement corrects a small number of misprint
Analysis of classical retrial queue with differentiated vacation and state dependent arrival rate.
In present paper we have introduced the concept of differentiated vacations in a retrial queueing model with state dependent arrival rates of customers. The arrival rate of customers is different in various states of the server. The vacation types are differentiated by means of their durations as well as the previous state of the server. In type I vacation, server goes just after providing service to at least one customer whereas in type II, it comes after remaining free for some time. In steady state, we have obtained the system size probabilities and other system performance measures. Finally, sensitivity and cost analysis of the proposed model is also performed. The probability generating function technique, parabolic method and MATLAB is used for the purpose
- …