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1.
We analyse a single-server retrial queueing system with infinite buffer, Poisson arrivals, general distribution of service
time and linear retrial policy. If an arriving customer finds the server occupied, he joins with probabilityp a retrial group (called orbit) and with complementary probabilityq a priority queue in order to be served. After the customer is served completely, he will decide either to return to the priority
queue for another service with probability ϑ or to leave the system forever with probability
=1−ϑ, where 0≤ϑ<1. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint
generating function of the number of customers in both groups in the steady-state regime. Moreover, we obtain the generating
function of system size distribution, which generalizes the well-knownPollaczek-Khinchin formula. Also we obtain a stochastic decomposition law for our queueing system and as an application we study the asymptotic behaviour
under high rate of retrials. The results agree with known special cases. Finally, we give numerical examples to illustrate
the effect of the parameters on several performance characteristics. 相似文献
2.
Abstract We concentrate on the analysis of the busy period and the waiting time distribution of a multi-server retrial queue in which primary arrivals occur according to a Markovian arrival process (MAP). Since the study of a model with an infinite retrial group seems intractable, we deal with a system having a finite buffer for the retrial group. The system is analyzed in steady state by deriving expressions for (a) the Laplace–Stieltjes transforms of the busy period and the waiting time; (b) the probabiliy generating functions for the number of customers served during a busy period and the number of retrials made by a customer; and (c) various moments of quantites of interest. Some illustrative numerical examples are discussed. 相似文献
3.
We consider anM/M/1 retrial queueing system in which the retrial time has a general distribution and only the customer at the head of the queue is allowed to retry for service. We find a necessary and sufficient condition for ergodicity and, when this is satisfied, the generating function of the distribution of the number of customers in the queue and the Laplace transform of the waiting time distribution under steady-state conditions. The results agree with known results for special cases.Supported by KOSEF 90-08-00-02. 相似文献
4.
In this paper, we investigate the impact of retrial phenomenon on loss probabilities and compare loss probabilities of several
channel allocation schemes giving higher priority to hand-off calls in the cellular mobile wireless network. In general, two
channel allocation schemes giving higher priority to hand-off calls are known; one is the scheme with the guard channels for
hand-off calls and the other is the scheme with the priority queue for hand-off calls. For mathematical unified model for
both schemes, we consider theMAP
1,MAP
2
/M/c/b, ∞ retrial queue with infinite retrial group, geometric loss, guard channels and finite priority queue for hand-off class.
We approximate the joint distribution of two queue lengths by Neuts' method and also obtain waiting time distribution for
hand-off calls. From these results, we obtain the loss probabilities, the mean waiting time and the mean queue lengths. We
give numerical examples to show the impact of the repeated attempt and to compare loss probabilities of channel allocation
schemes. 相似文献
5.
In this paper, we consider a c-server queuing model in which customers arrive according to a batch Markovian arrival process (BMAP). These customers are served in groups of varying sizes ranging from a predetermined value L through a maximum size, K. The service times are exponentially distributed. Any customer not entering into service immediately orbit in an infinite space. These orbiting customers compete for service by sending out signals that are exponentially distributed with parameter . Under a full access policy freed servers offer services to orbiting customers in groups of varying sizes. This multi-server retrial queue under the full access policy is a QBD process and the steady state analysis of the model is performed by exploiting the structure of the coefficient matrices. Some interesting numerical examples are discussed. 相似文献
6.
Evsey Morozov 《Queueing Systems》2007,56(3-4):157-168
We consider a multiserver retrial GI/G/m queue with renewal input of primary customers, interarrival time τ with rate
, service time S, and exponential retrial times of customers blocked in the orbit. In the model, an arriving primary customer enters the system
and gets a service immediately if there is an empty server, otherwise (if all m servers are busy) he joins the orbit and attempts to enter the system after an exponentially distributed time. Exploiting
the regenerative structure of the (non-Markovian) stochastic process representing the total number of customers in the system
(in service and in orbit), we determine stability conditions of the system and some of its variations. More precisely, we
consider a discrete-time process embedded at the input instants and prove that if
and
, then the regeneration period is aperiodic with a finite mean. Consequently, this queue has a stationary distribution under
the same conditions as a standard multiserver queue GI/G/m with infinite buffer. To establish this result, we apply a renewal technique and a characterization of the limiting behavior
of the forward renewal time in the (renewal) process of regenerations. The key step in the proof is to show that the service
discipline is asymptotically work-conserving as the orbit size increases. Included are extensions of this stability analysis
to continuous-time processes, a retrial system with impatient customers, a system with a general retrial rate, and a system
with finite buffer for waiting primary customers. We also consider the regenerative structure of a multi-dimensional Markov
process describing the system.
This work is supported by Russian Foundation for Basic Research under grants 04-07-90115 and 07-07-00088. 相似文献
7.
In this paper, we consider a Geo/Geo/1 retrial queue with non-persistent customers and working vacations. The server works at a lower service rate in a working vacation period. Assume that the customers waiting in the orbit request for service with a constant retrial rate, if the arriving retrial customer finds the server busy, the customer will go back to the orbit with probability q (0≤q≤1), or depart from the system immediately with probability $\bar{q}=1-q$ . Based on the necessary and sufficient condition for the system to be stable, we develop the recursive formulae for the stationary distribution by using matrix-geometric solution method. Furthermore, some performance measures of the system are calculated and an average cost function is also given. We finally illustrate the effect of the parameters on the performance measures by some numerical examples. 相似文献
8.
In this paper a queueing system in which work gets postponed due to finiteness of the buffer is considered. When the buffer
is full (capacityK) further arrivals are directed to a pool of customers (postponed work). An arrival encountering the buffer full, will join
the pool with probability γ (0<γ<1); else it is lost to the system forever. When, at a departure epoch the buffer size drops
to a preassigned levelL−1 (1<L<K) or below, a postponed work is transferred with probabilityp (0<p<1) and positioned as the last among the waiting customers. If at a service completion epoch the buffer turns out to be empty
and there is at least one customer in the pool, then the one ahead of all waiting in the pool gets transferred (with probability
one) to the buffer and its service commences immediately. This ensures conservation of work. With arrival forming a Poisson
process and service time having PH-distribution we study the long run behaviour of the system. Several system performance
measures are obtained. A control problem is discussed and some numerical illustrations are provided. 相似文献
9.
The equilibrium and socially optimal balking strategies are investigated for unobservable and observable single-server classical retrial queues. There is no waiting space in front of the server. If an arriving customer finds the server idle, he occupies the server immediately and leaves the system after service. Otherwise, if the server is found busy, the customer decides whether or not to enter a retrial pool with infinite capacity and becomes a repeated customer, based on observation of the system and the reward–cost structure imposed on the system. Accordingly, two cases with respect to different levels of information are studied and the corresponding Nash equilibrium and social optimization balking strategies for all customers are derived. Finally, we compare the equilibrium and optimal behavior regarding these two information levels through numerical examples. 相似文献
10.
Summary This paper is concerned with the study of a newM/G/1 retrial queueing system in which the delays between retrials are exponentially distributed random variables with linear intensityg(n)=α+nμ, when there aren≥1 customers in the retrial group. This new retrial discipline will be calledlinear control policy. We carry out an extensive analysis of the model, including existence of stationary regime, stationary distribution of the
embedded Markov chain at epochs of service completions, joint distribution of the orbit size and the server state in steady
state and busy period. The results agree with known results for special cases. 相似文献
11.
We consider the M/M/s/K retrial queues in which a customer who is blocked to enter the service facility may leave the system with a probability that depends on the number of attempts of the customer to enter the service facility. Approximation formulae for the distributions of the number of customers in service facility, waiting time in the system and the number of retrials made by a customer during its waiting time are derived. Approximation results are compared with the simulation. 相似文献
12.
We consider a single server retrial queue with waiting places in service area and three classes of customers subject to the server breakdowns and repairs. When the server is unavailable, the arriving class-1 customer is queued in the priority queue with infinite capacity whereas class-2 customer enters the retrial group. The class-3 customers which are also called negative customers do not receive service. If the server is found serving a customer, the arriving class-3 customer breaks the server down and simultaneously deletes the customer under service. The failed server is sent to repair immediately and after repair it is assumed as good as new. We study the ergodicity of the embedded Markov chains and their stationary distributions. We obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law, the busy period of the system and the virtual waiting times. Finally, an application to cellular mobile networks is provided and the effects of various parameters on the system performance are analyzed numerically. 相似文献
13.
Yang Woo Shin 《Journal of Applied Mathematics and Computing》2000,7(1):83-100
Many queueing systems such asM/M/s/K retrial queue with impatient customers, MAP/PH/1 retrial queue, retrial queue with two types of customers andMAP/M/∞ queue can be modeled by a level dependent quasi-birth-death (LDQBD) process with linear transition rates of the form λk = α+ βk at each levelk. The purpose of this paper is to propose an algorithm to find transient distributions for LDQBD processes with linear transition rates based on the adaptive uniformizaton technique introduced by van Moorsel and Sanders [11]. We apply the algorithm to some retrial queues and present numerical results. 相似文献
14.
Peter Sendfeld 《Methodology and Computing in Applied Probability》2008,10(4):557-558
We consider an open queueing network consisting of two queues with Poisson arrivals and exponential service times and having
some overflow capability from the first to the second queue. Each queue is equipped with a finite number of servers and a
waiting room with finite or infinite capacity. Arriving customers may be blocked at one of the queues depending on whether
all servers and/or waiting positions are occupied. Blocked customers from the first queue can overflow to the second queue
according to specific overflow routines. Using a separation method for the balance equations of the two-dimensional server
and waiting room demand process, we reduce the dimension of the problem of solving these balance equations substantially.
We extend the existing results in the literature in three directions. Firstly, we allow different service rates at the two
queues. Secondly, the overflow stream is weighted with a parameter p ∈ [0,1], i.e., an arriving customer who is blocked and overflows, joins the overflow queue with probability p and leaves the system with probability 1 − p. Thirdly, we consider several new blocking and overflow routines.
An erratum to this article can be found at 相似文献
15.
In this paper, aK classM/G/1 queueing system with feedback is examined. Each arrival requires at least one, and possibly up toK service phases. A customer is said to be in classk if it is waiting for or receiving itskth phase of service. When a customer finishes its phasek ≤K service, it either leaves the system with probabilityp
k, or it instantaneously reenters the system as a classk + 1 customer with probability (1 −p
k). It is assumed thatp
k = 1. Service is non-preemptive and FCFS within a specified priority ordering of the customer classes. Level crossing analysis
of queues and delay cycle results are used to derive the Laplace-Stieltjes Transform (LST) for the PDF of the sojourn time
in classes 1,…,k;k ≤K. 相似文献
16.
We consider an M/G/1 retrial queue where the service time distribution has a regularly varying tail with index −β, β>1. The waiting time distribution is shown to have a regularly varying tail with index 1−β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue
with the waiting time in the ordinary M/G/1 queue with random order service policy. 相似文献
17.
This paper gives a transient analysis of the classic M/M/1 and M/M/1/K queues. Our results are asymptotic as time and queue length become simultaneously large for the infinite capacity queue, and as the system’s storage capacity K becomes large for the finite capacity queue. We give asymptotic expansions for pn(t), which is the probability that the system contains n customers at time t. We treat several cases of initial conditions and different traffic intensities. The results are based on (i) asymptotic expansion of an exact integral representation for pn(t) and (ii) applying the ray method to a scaled form of the forward Kolmogorov equation which describes the time evolution of pn(t). 相似文献
18.
This paper considers theM/M/c queue in which a customer leaves when its service has not begun within a fixed interval after its arrival. The loss probability
can be expressed in a simple formula involving the waiting time probabilities in the standardM/M/c queue. The purpose of this paper is to give a probabilistic derivation of this formula and to outline a possible use of this
general formula in theM/M/c retrial queue with impatient customers.
This research was supported by the INTAS 96-0828 research project and was presented at the First International Workshop on
Retrial Queues, Universidad Complutense de Madrid, Madrid, September 22–24, 1998. 相似文献
19.
This paper investigates a batch arrival retrial queue with general retrial times, where the server is subject to starting failures and provides two phases of heterogeneous service to all customers under Bernoulli vacation schedules. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of two phases of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1 − p). We construct the mathematical model and derive the steady-state distribution of the server state and the number of customers in the system/orbit. Such a model has potential application in transfer model of e-mail system. 相似文献
20.
This paper deals with the steady state behaviour of an MX/G/1 retrial queue with an additional second phase of optional service and unreliable server where breakdowns occur randomly at any instant while serving the customers. Further concept of Bernoulli admission mechanism is also introduced in the model. This model generalizes both the classical MX/G/1 retrial queue subject to random breakdown and Bernoulli admission mechanism as well as MX/G/1 queue with second optional service and unreliable server. We carry out an extensive analysis of this model. 相似文献