共查询到20条相似文献,搜索用时 0 毫秒
1.
Jesus R. Artalejo Antonis Economou Antonio Gómez-Corral 《European Journal of Operational Research》2008
In this paper, we consider a discrete-time queue of Geo/Geo/c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/M/c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused from the retrial feature. In discrete-time, the occurrence of multiple events at each slot increases the complexity of the model and raises further computational difficulties. We propose several algorithmic procedures for the efficient computation of the main performance measures of this system. More specifically, we investigate the stationary distribution of the system state, the busy period and the waiting time. Several numerical examples illustrate the analysis. 相似文献
2.
M. J. Lopez-Herrero 《Annals of Operations Research》2006,141(1):271-281
This paper concerns the busy period of a single server queueing model with exponentially distributed repeated attempts. Several
authors have analyzed the structure of the busy period in terms of the Laplace transform but, the information about the density
function is limited to first and second order moments. We use the maximum entropy principle to find the least biased density
function subject to several mean value constraints. We perform results for three different service time distributions: 3-stage
Erlang, hyperexponential and exponential. Also a numerical comparative analysis between the exact Laplace transform and the
corresponding maximum entropy density is presented.
AMS subject classification: 90B05 90B22 相似文献
3.
In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian
arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some
interesting numerical examples are presented. 相似文献
4.
We study a GI/M/1 queue with an N threshold policy. In this system, the server stops attending the queue when the system becomes empty and resumes serving the queue when the number of customers reaches a threshold value N. Using the embeded Markov chain method, we obtain the stationary distributions of queue length and waiting time and prove the stochastic decomposition properties. 相似文献
5.
This paper studies a fluid model driven by an M/G/1 queue with multiple exponential vacations. By introducing various vacation strategies to the fluid model, we can provide greater flexibility for the design and control of input rate and output rate. The Laplace transform of the steady-state distribution of the buffer content is expressed through the minimal positive solution to a crucial equation. Then the performance measure-mean buffer content, which is independent of the vacation parameter, is obtained. Finally, with some numerical examples, the parameter effect on the mean buffer content is presented. 相似文献
6.
Refik Güllü 《Operations Research Letters》2004,32(5):431-438
We analyze an M/G/∞ queue with batch arrivals, where jobs belonging to a batch have to be processed by the same server. The number of jobs in the system is characterized as a compound Poisson random variable through a scaling of the original arrival and batch size processes. 相似文献
7.
We consider finite buffer single server GI/M/1 queue with exhaustive service discipline and multiple working vacations. Service times during a service period, service times during a vacation period and vacation times are exponentially distributed random variables. System size distributions at pre-arrival and arbitrary epoch with some important performance measures such as, probability of blocking, mean waiting time in the system etc. have been obtained. The model has potential application in the area of communication network, computer systems etc. where a single channel is allotted for more than one source. 相似文献
8.
9.
The purpose of this corrigendum is two-fold. First, we acknowledge that two results in our paper (Novak et al. in Queueing
Syst. 53:105–114, 2006) can be obtained from earlier results of Prabhu and Bhat. Second, we make corrections to Theorem 2.2, Corollary 2.1 and Theorem 4.2
of Novak et al. (Queueing Syst. 53:105–114, 2006).
相似文献
10.
We consider a discrete-time single server N -policy GI/Geo/1 queueing system. The server stops servicing whenever the system becomes empty, and resumes its service as soon as the number of waiting customers in the queue reaches N. Using an embedded Markov chain and a trial solution approach, the stationary queue length distribution at arrival epochs is obtained. Furthermore, we obtain the stationary queue length distribution at arbitrary epochs by using the preceding result and a semi-Markov process. The sojourn time distribution is also presented. 相似文献
11.
An M/G/1 retrial queueing system with disasters and unreliable server is investigated in this paper. Primary customers arrive in the system according to a Poisson process, and they receive service immediately if the server is available upon their arrivals. Otherwise, they will enter a retrial orbit and try their luck after a random time interval. We assume the catastrophes occur following a Poisson stream, and if a catastrophe occurs, all customers in the system are deleted immediately and it also causes the server’s breakdown. Besides, the server has an exponential lifetime in addition to the catastrophe process. Whenever the server breaks down, it is sent for repair immediately. It is assumed that the service time and two kinds of repair time of the server are all arbitrarily distributed. By applying the supplementary variables method, we obtain the Laplace transforms of the transient solutions and also the steady-state solutions for both queueing measures and reliability quantities of interest. Finally, numerical inversion of Laplace transforms is carried out for the blocking probability of the system, and the effects of several system parameters on the blocking probability are illustrated by numerical inversion results. 相似文献
12.
Peter Hall 《Stochastic Processes and their Applications》1985,19(2):259-269
A necessary and sufficient condition is given for busy period in an M/G/∞ queue to be asymptotically exponential with mean equal to expected busy period, as traffic intensity increases. The case where this condition fails is also investigated, and the results applied. 相似文献
13.
In this paper, we study the transient behavior of a state dependent M/M/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. For two special cases called the threshold policy and the static policy we determine simple expressions for their joint transform. 相似文献
14.
We compute in this paper the distribution of the area
swept under the occupation process of an M/M/1 queue during a busy period. For this purpose, we use the expression of the Laplace transform
of the random variable
established in earlier studies as a fraction of Bessel functions. To get information on the poles and the residues of
, we take benefit of the fact that this function can be represented by a continued fraction. We then show that this continued
fraction is the even part of an S fraction and we identify its successive denominators by means of Lommel polynomials. This allows us to numerically evaluate
the poles and the residues. Numerical evidence shows that the poles are very close to the numbers
as
. This motivated us to formulate some conjectures, which lead to the derivation of the asymptotic behaviour of the poles and
the residues. This is finally used to derive the asymptotic behaviour of the probability survivor function
. The outstanding property of the random variable
is that the poles accumulate at 0 and its tail does not exhibit a nice exponential decay but a decay of the form
for some positive constants c and
, which indicates that the random variable
has a Weibull-like tail.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
The purpose of this note is to correct an error in Baltrunas et al. (2004) [1], and to give a more detailed argument to a formula whose validity has been questioned over the years. These details close a gap in the proof of Theorem 4.1 as originally stated, the validity of which is hereby strengthened. 相似文献
16.
T. Kimura 《Mathematical and Computer Modelling》1995,22(10-12)
This paper develops approximations for the delay probability in an M/G/s queue. For M/G/s queues, it has been well known that the delay probability in the M/M/s queue, i.e., the Erlang delay formula, is usually a good approximation for other service-time distributions. By using an excellent approximation for the mean waiting time in the M/G/s queue, we provide more accurate approximations of the delay probability for small values of s. To test the quality of our approximations, we compare them with the exact value and the Erlang delay formula for some particular cases. 相似文献
17.
We consider an M/PH/1 queue with workload-dependent balking. An arriving customer joins the queue and stays until served if and only if the system
workload is no more than a fixed level at the time of his arrival. We begin by considering a fluid model where the buffer
content changes at a rate determined by an external stochastic process with finite state space. We derive systems of first-order
linear differential equations for the mean and LST (Laplace-Stieltjes Transform) of the busy period in this model and solve
them explicitly. We obtain the mean and LST of the busy period in the M/PH/1 queue with workload-dependent balking as a special limiting case of this fluid model. We illustrate the results with numerical
examples.
相似文献
18.
Bidisha Borkakaty Kanwar Sen Manju Agarwal 《Mathematical and Computer Modelling》2009,50(7-8):1067-1082
In this paper, we find the busy period density of queues in explicit computational form, through lattice path (LP) approach. Both the arrival and service time distributions are approximated by 2-phase Cox distribution C2, which has a Markovian property enabling us to use LP combinatorics. Since any distribution with rational Laplace–Stieltjes transform (LST) and square coefficient of variation (CV2) lying in [1/2,∞) can be approximated by a C2([M. Agarwal, K. Sen, B. Borkakaty, Busy period density of queueing system C3/M/1, Journal of Combinatorics, Information and Systems Sciences 31 (1–4) (2006) 127–161]), the results obtained would be applicable to a very wide class of distributions occurring in real life. 相似文献
19.
This note considers the N- and D-policies for the M/G/1 queue. We concentrate on the true relationship between the optimal N- and D-policies when the cost function is based on the expected number of customers in the system. 相似文献
20.
In this paper, we consider a discrete-time finite-capacity queue with Bernoulli arrivals and batch services. In this queue, the single server has a variable service capacity and serves the customers only when the number of customers in system is at least a certain threshold value. For this queue, we first obtain the queue-length distribution just after a service completion, using the embedded Markov chain technique. Then we establish a relationship between the queue-length distribution just after a service completion and that at a random epoch, using elementary ‘rate-in = rate-out’ arguments. Based on this relationship, we obtain the queue-length distribution at a random (as well as at an arrival) epoch, from which important performance measures of practical interest, such as the mean queue length, the mean waiting time, and the loss probability, are also obtained. Sample numerical examples are presented at the end. 相似文献