Topic
Retrial queue
About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.
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TL;DR: A finite buffer capacity GI/GI/c/K-type retrial queueing system with constant retrial rate with sufficient stability conditions is considered, which covers a number of new particular cases with the closed-form stability conditions.
Abstract: We consider a GI/G/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has $c$ identical servers and can accommodate the maximal number of $K$ jobs. If a newly arriving job finds the full primary queue, it joins the orbit. The original primary jobs arrive to the system according to a renewal process. The jobs have general i.i.d. service times. A job in front of the orbit queue retries to enter the primary queue after an exponentially distributed time independent of the orbit queue length. Telephone exchange systems, Medium Access Protocols and short TCP transfers are just some applications of the proposed queueing system. For this system we establish minimal sufficient stability conditions. Our model is very general. In addition, to the known particular cases (e.g., M/G/1/1 or M/M/c/c systems), the proposed model covers as particular cases the deterministic service model and the Erlang model with constant retrial rate. The latter particular cases have not been considered in the past. The obtained stability conditions have clear probabilistic interpretation.
15 citations
TL;DR: The present investigation deals with the bulk arrival M/G/1 retrial queue with impatient customers and modified vacation policy, where the incoming customers are impatient and may renege on seeing a long queue of the customers for the service.
Abstract: The present investigation deals with the bulk arrival M/G/1 retrial queue with impatient customers and modified vacation policy. The incoming customers join the virtual pool of customers called orbit if they find the server being busy, on vacation or in broken down state otherwise the service of the customer at the head of the batch is started by the server. The service is provided in k essential phases to all the customers by the single server which may breakdown while rendering service to the customers. The broken down server is sent to a repair facility wherein the repair is performed in d compulsory phases. As soon as the orbit becomes empty, the server goes for vacation and takes at most J vacations until at least one customer is noticed. The incoming customers are impatient and may renege on seeing a long queue of the customers for the service. The probability generating functions and queue length for the number of customers in the orbit and queue have been obtained using supplementary variable technique. Various system characteristics viz. average number of customers in the queue and the orbit, long run probabilities of the system states, etc. are obtained. Furthermore, numerical simulation has been carried out to study the sensitivity of various parameters on the system performance measures by taking an illustration.
15 citations
TL;DR: In this paper, the authors present a recursive method of computation for the probability that at most k customers were served during the busy period of an M/G/1 retrial queue.
Abstract: We present a recursive method of computation for the probability that at most k customers were served during the busy period of an M/G/1 retrial queue.
15 citations
18 Sep 2014
TL;DR: The authors illustrate numerical results of the delay, throughput and spectrum occupancy with respect to retrial rate, spectrum sensing time and primary user's busy rate.
Abstract: The authors apply the preemptive priority queueing analysis to cognitive radio networks. Using the proposed analytical model, the authors can quantify the delay, throughput and spectrum occupancy of cognitive radio networks. Cognitive users’ packet arrivals form a retrial queue with a proper choice of the retrial rate. The authors illustrate numerical results of the delay, throughput and spectrum occupancy with respect to retrial rate, spectrum sensing time and primary user's busy rate.
14 citations
TL;DR: A quasi birth and death process is used to describe the considered system and a condition for the stability of the model is derived to prove the conditional stochastic decomposition for the queue length in the orbit.
Abstract: Consider an M/M/1 retrial queue with collisions and working vacation interruption under N-policy. We use a quasi birth and death process to describe the considered system and derive a condition for the stability of the model. Using the matrix-analytic method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, some numerical examples are presented.
14 citations