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1.
We consider anM/G/1 priority retrial queueing system with two types of calls which models a telephone switching system and a cellular mobile communication system. In the case that arriving calls are blocked due to the server being busy, type I calls are queued in a priority queue of finite capacityK whereas type II calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form. When 1=0, it is shown that our results are consistent with the known results for a classical retrial queueing system. 相似文献
2.
We consider a discrete-time Geo/G/1 retrial queue in which 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 study the Markov chain underlying the considered queueing system and its ergodicity condition. We find the generating function of the number of customers in the orbit and in the system. We derive the stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions for our queueing system and its corresponding standard system. Also, we develop recursive formulae for calculating the steady-state distribution of the orbit and system sizes. Besides, we prove that the M/G/1 retrial queue with general retrial times can be approximated by our corresponding discrete-time system. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics. 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.
We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If
both queues are nonempty, a customer of queue 1 is served with probability β, and a customer of queue 2 is served with probability 1−β. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating
function U(z
1,z
2) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary
value problems. Then, we propose to use the same functional equation to obtain a power series for U(z
1,z
2) in β. The first coefficient of this power series corresponds to the priority case β=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations
for the mean stationary queue lengths are obtained from combining truncated power series and Padé approximation. 相似文献
5.
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
6.
We consider anM/G/1 retrial queue with infinite waiting space in which arriving customers who find the server busy join either (a) the retrial group with probabilityp in order to seek service again after a random amount of time, or (b) the infinite waiting space with probabilityq(=1–p) where they wait to be served. The joint generating function of the numbers of customers in the two groups is derived by using the supplementary variable method. It is shown that our results are consistent with known results whenp=0 orp=1. 相似文献
7.
Vyacheslav M Abramov 《Annals of Operations Research》2006,141(1):19-50
The paper studies a multiserver retrial queueing system withm 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 μ1. A time between retrials is exponentially distributed with parameter μ2 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 μ2 increases to infinity. As μ2→∞, 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.
AMS 2000 Subject classifications: 60K25 60H30. 相似文献
8.
Sofian De Clercq Bart Steyaert Herwig Bruneel 《4OR: A Quarterly Journal of Operations Research》2012,10(1):67-79
This paper introduces a new priority mechanism in discrete-time queueing systems that compromises between first-come-first-served
(FCFS) and head-of-line priority. In this scheduling discipline—which we dubbed slot-bound priority—customers of different
priority classes entering the system during the same time-slot are served in order of their respective priority class. Customers
entering during different slots are served on a FCFS basis. In this paper we study the delay in an N-class discrete-time queueing system under slot-bound priority. General independent arrivals and class-specific general service
time distributions are assumed. Expressions for the probability generating function of the delay of a random type-j customer are derived, from which the respective moments are easily obtained. The tail behaviour of these distributions is
analyzed as well, and some numerical examples show the effect slot-bound priority can have on the performance measures. 相似文献
9.
G. I. Falin 《Queueing Systems》2008,58(3):155-160
Sherman and Kharoufeh (Oper. Res. Lett. 34:697–705, [2006]) considered an M/M/1 type queueing system with unreliable server and retrials. In this model it is assumed that if the server fails during service
of a customer, the customer leaves the server, joins a retrial group and in random intervals repeats attempts to get service.
We suggest an alternative method for analysis of the Markov process, which describes the functioning of the system, and find
the joint distribution of the server state, the number of customers in the queue and the number of customers in the retrial
group in steady state.
相似文献
10.
11.
This paper is concerned with a discrete-time Geo/G/1 retrial queue with preferred, impatient customers and general retrial times. We analyze the Markov chain underlying the considered queueing system and derive its ergodicity condition. The system state distribution as well as the orbit size and the system size distributions are obtained in terms of their generating functions. These generating functions yield exact expressions for different performance measures. Besides, the stochastic decomposition property and the corresponding continuous-time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of priority and impatience on several performance characteristics of the system. 相似文献
12.
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
13.
This paper deals with a multi-class priority queueing system with customer transfers that occur only from lower priority queues
to higher priority queues. Conditions for the queueing system to be stable/unstable are obtained. An auxiliary queueing system
is introduced, for which an explicit product-form solution is found for the stationary distribution of queue lengths. Sample
path relationships between the queue lengths in the original queueing system and the auxiliary queueing system are obtained,
which lead to bounds on the stationary distribution of the queue lengths in the original queueing system. Using matrix-analytic
methods, it is shown that the tail asymptotics of the stationary distribution is exact geometric, if the queue with the highest
priority is overloaded.
相似文献
14.
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
15.
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
16.
In queueing theory, an important class of events can be written as ‘infinite intersections’. For instance, in a queue with
constant service rate c, busy periods starting at 0 and exceeding L > 0 are determined by the intersection of the events
, i.e., queue Q
t
is empty at 0 and for all t∊ [0, L] the amount of traffic A
t
arriving in [0,t) exceeds the server capacity. Also the event of exceeding some predefined threshold in a tandem queue, or a priority queue,
can be written in terms of this kind of infinite intersections. This paper studies the probability of such infinite intersections
in queueing systems fed by a large number n of i.i.d. traffic sources (the so-called ‘many-sources regime’). If the sources are of the exponential on-off type, and the
queueing resources are scaled proportional to n, the probabilities under consideration decay exponentially; we explicitly characterize the corresponding decay rate. The
techniques used stem from large deviations theory (particularly sample-path large deviations).
M. Mandjes is also with Korteweg-de Vries Institute, University of Amsterdam, Amsterdam, the Netherlands, and EURANDOM, Eindhoven,
the Netherlands.
Work done while P. Mannersalo was on leave at CWI.
MSC 2000: 60F10 (Large deviations), 60K25 (Queueing theory) 相似文献
17.
18.
19.
We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and
the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach
the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the
call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per
time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always
sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition.
In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady
state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent
i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence
to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival
and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service
and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential
bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions
for boundedness in distribution for the case of nonpatient (or non persistent) customers.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
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