It is well known that discrete-time queues are more appropiate than their
continuous-time counterparts for modelling computer and telecommunication
systems. We present a discrete-time Geo/G/1 retrial queue with general retrial
times, Bernoulli feedback and the server subjected to starting failures. We gene-
ralize the previous works in discrete{time retrial queue with unrealiable server
due to starting failures in the sense that we consider general service and ge-
neral retrial times. Also we consider the realistic phenomenon of feedback. We
analyse the Markov chain underlying the considered queueing system and pre-
sent some performance measures of the system in steady-state. We provide two
stochastic decomposition laws. Besides, we prove that the M/G/1 retrial queue
with feedback and starting failures can be approximated by our corresponding
discrete-time system. Some numerical results are given to illustrate the impact
of the unreability and the feedback on the performance of the syste

A discrete-time retrial queueing system with starting failures, Bernoulli feedback and general retrial times

We analyze a discrete-time Geo[X]/G/1 retrial queue where the retrial time has a general distribution,and the server, after each service completion,begins a process of search in order to find the following customer to be served.We assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline and only the customer at the head of the queue is allowed for access to the server.We derive analytical results for the queue length distribution as well as some performance measures of the system under steady state condition.It is proved that the M[X]/G/1 retrial queue with general retrial times can be approximated by our corresponding discrete-time system.

Discrete-time retrial queue with general retrial times

We consider a discrete-time Geo/G/1 queue with general retrial times, balking customers, feedback, and starting failures of the server. We analyze the Markov chain underlying the considered queueing system and present some performance measures of the system in steady-state. Numerical results are presented with a focus on the effect of feedback and balking on the system performance.

http://ieeexplore.ieee.org/iel5/5379694/5380897/05380911.pdf

A Discrete Time Geo/G/1 Retrial Queue with Balking, Feedback and Starting Failures

We consider a discrete-time Geo/G/1 retrial queue with feedback, balking customers, and general retrial times. If a new arriving customer finds the server busy, he may depart immediately from the system or join the orbit. After service completion, the customer decides either to join the orbit for another service or leaves the system completely. We analyze the Markov chain underlying the considered queueing system and present some performance measures of the system in steady-state. Numerical results show how sensitive the system performance measures are when parameters of the system change.

Yi-juan Zhu

Papers

A Discrete Time Geo/G/1 Retrial Queue with Balking, Feedback and Starting Failures

A Discrete Time Geo/G/1 Queue with Feedback, Balking and General Retrial Times