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1.
We consider a discrete time single server queueing system where the arrival process is governed by a discrete autoregressive
process of order p (DAR(p)), and the service time of a customer is one slot. For this queueing system, we give an expression for the mean queue size,
which yields upper and lower bounds for the mean queue size. Further we propose two approximation methods for the mean queue
size. One is based on the matrix analytic method and the other is based on simulation. We show, by illustrations, that the
proposed approximations are very accurate and computationally efficient. 相似文献
2.
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
3.
We study a discrete-time GI/Geo/1 queue with server vacations. In this queueing system, the server takes vacations when the system does not have any waiting customers at a service completion instant or a vacation completion instant. This type of discrete-time queueing model has potential applications in computer or telecommunication network systems. Using matrix-geometric method, we obtain the explicit expressions for the stationary distributions of queue length and waiting time and demonstrate the conditional stochastic decomposition property of the queue length and waiting time in this system. 相似文献
4.
Using recursive method,this paper studies the queue size properties at any epoch n + in Geom/G/1(E,SV) queueing model with feedback under LASDA (late arrival system with delayed access) setup.Some new results about the recursive expressions of queue size distribution at different epoch (n+,n,n-) are obtained.Furthermore the important relations between stationary queue size distribution at different epochs are discovered.The results are different from the relations given in M/G/1 queueing system.The model discussed in this paper can be widely applied in many kinds of communications and computer network. 相似文献
5.
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
6.
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
7.
One of the key performance measures in queueing systems is the decay rate of the steady-state tail probabilities of the queue
lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have finite moments, then
the queue lengths also have finite moments, so that the tail probability ℙ(⋅>s) decays faster than s
−n
for any n. It is natural to conjecture that the decay rate is in fact exponential. 相似文献
8.
We study a GI/M/c type queueing system with vacations in which all servers take vacations together when the system becomes empty. These servers keep taking synchronous vacations until they find waiting customers in the system at a vacation completion instant.The vacation time is a phase-type (PH) distributed random variable. Using embedded Markov chain modeling and the matrix geometric solution methods, we obtain explicit expressions for the stationary probability distributions of the queue length at arrivals and the waiting time. To compare the vacation model with the classical GI/M/c queue without vacations, we prove conditional stochastic decomposition properties for the queue length and the waiting time when all servers are busy. Our model is a generalization of several previous studies. 相似文献
9.
We consider a GI/G/1 queue in which the service time distribution and/or the interarrival time distribution has a heavy tail,
i.e., a tail behaviour like t
−ν with 1 < ν ⩽ 2 , so that the mean is finite but the variance is infinite. We prove a heavy-traffic limit theorem for the
distribution of the stationary actual waiting time W. If the tail of the service time distribution is heavier than that of the interarrival time distribution, and the traffic
load a → 1, then W, multiplied by an appropriate ‘coefficient of contraction’ that is a function of a, converges in distribution to the Kovalenko distribution. If the tail of the interarrival time distribution is heavier than
that of the service time distribution, and the traffic load a → 1, then W, multiplied by another appropriate ‘coefficient of contraction’ that is a function of a, converges in distribution to the negative exponential distribution.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
10.
Motivated by applications in manufacturing systems and computer networks, in this paper, we consider a tandem queue with feedback.
In this model, the i.i.d. interarrival times and the i.i.d. service times are both exponential and independent. Upon completion
of a service at the second station, the customer either leaves the system with probability p or goes back, together with all customers currently waiting in the second queue, to the first queue with probability 1−p. For any fixed number of customers in one queue (either queue 1 or queue 2), using newly developed methods we study properties
of the exactly geometric tail asymptotics as the number of customers in the other queue increases to infinity. We hope that
this work can serve as a demonstration of how to deal with a block generating function of GI/M/1 type, and an illustration
of how the boundary behaviour can affect the tail decay rate. 相似文献
11.
Louiza Bouallouche-Medjkoune Djamil Aissani 《Mathematical Methods of Operations Research》2006,63(2):341-356
In this work, we apply the strong stability method to obtain an estimate for the proximity of the performance measures in the M/G/1 queueing system to the same performance measures in the M/M/1 system under the assumption that the distributions of the service time are close and the arrival flows coincide. In addition to the proof of the stability fact for the perturbed M/M/1 queueing system, we obtain the inequalities of the stability. These results give with precision the error, on the queue size stationary distribution, due to the approximation. For this, we elaborate from the obtained theoretical results, the STR-STAB algorithm which we execute for a determined queueing system: M/Coxian − 2/1. The accuracy of the approach is evaluated by comparison with simulation results. 相似文献
12.
In this paper, we present a detailed analysis of a cyclic-service queueing system consisting of two parallel queues, and a
single server. The server serves the two queues with a Bernoulli service schedule described as follows. At the beginning of
each visit to a queue, the server always serves a customer. At each epoch of service completion in the ith queue at which the queue is not empty, the server makes a random decision: with probability pi, it serves the next customer; with probability 1-pi, it switches to the other queue. The server takes switching times in its transition from one queue to the other. We derive
the generating functions of the joint stationary queue-length distribution at service completion instants, by using the approach
of the boundary value problem for complex variables. We also determine the Laplace-Stieltjes transforms of waiting time distributions
for both queues, and obtain their mean waiting times.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time W in the GI/GI/2 FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics
are given for the probability P{W > x}. We also get asymptotics for the distribution tail of a stationary two-dimensional workload vector and of a stationary queue
length. These asymptotics depend heavily on the traffic load.
AMS subject classification: 60K25 相似文献
14.
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
15.
Relay nodes in an ad hoc network can be modelled as fluid queues, in which the available service capacity is shared by the
input and output. In this paper such a relay node is considered; jobs arrive according to a Poisson process and bring along
a random amount of work. The total transmission capacity is fairly shared, meaning that, when n jobs are present, each job transmits traffic into the queue at rate 1/(n + 1) while the queue is drained at the same rate of 1/(n + 1). Where previous studies mainly concentrated on the case of exponentially distributed job sizes, the present paper addresses
regularly varying jobs. The focus lies on the tail asymptotics of the sojourn time S. Using sample-path arguments, it is proven that ${\mathbb{P}\left\{ S > x \right\}}${\mathbb{P}\left\{ S > x \right\}} behaves roughly as the residual job size, i.e., if the job sizes are regularly varying of index − ν, the tail of S is regularly varying of index 1 − ν In addition, we address the tail asymptotics of other performance metrics, such as the workload in the queue, the flow transfer
time and the queueing delay. 相似文献
16.
We consider a MAP/G/1 retrial queue where the service time distribution has a finite exponential moment. We derive matrix differential equations
for the vector probability generating functions of the stationary queue size distributions. Using these equations, Perron–Frobenius
theory, and the Karamata Tauberian theorem, we obtain the tail asymptotics of the queue size distribution. The main result
on light-tailed asymptotics is an extension of the result in Kim et al. (J. Appl. Probab. 44:1111–1118, 2007) on the M/G/1 retrial queue. 相似文献
17.
The paper investigates the queueing process in stochastic systems with bulk input, batch state dependent service, server vacations,
and three post-vacation disciplines. The policy of leaving and entering busy periods is hysteretic, meaning that, initially,
the server leaves the system on multiple vacation trips whenever the queue falls below r (⩾1), and resumes service when during his absence the system replenishes to N or more customers upon one of his returns. During his vacation trips, the server can be called off on emergency, limiting
his trips by a specified random variable (thereby encompassing several classes of vacation queues, such as ones with multiple
and single vacations). If by then the queue has not reached another fixed threshold M (⩽ N), the server enters a so-called “post-vacation period” characterized by three different disciplines: waiting, or leaving
on multiple vacation trips with or without emergency. For all three disciplines, the probability generating functions of the
discrete and continuous time parameter queueing processes in the steady state are obtained in a closed analytic form. The
author uses a semi-regenerative approach and enhances fluctuation techniques (from his previous studies) preceding the analysis
of queueing systems. Various examples demonstrate and discuss the results obtained.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
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
19.
M. R. Salehirad A. Badamchizadeh 《Central European Journal of Operations Research》2009,17(2):131-139
In this paper we consider an M/G/1 queue with k phases of heterogeneous services and random feedback, where the arrival is Poisson and service times has general
distribution. After the completion of the i-th phase, with probability θ
i
the (i + 1)-th phase starts, with probability p
i
the customer feedback to the tail of the queue and with probability 1 − θ
i
− p
i
= q
i
departs the system if service be successful, for i = 1, 2 , . . . , k. Finally in kth phase with probability p
k
feedback to the tail of the queue and with probability 1 − p
k
departs the system. We derive the steady-state equations, and PGF’s of the system is obtained. By using them the mean queue
size at departure epoch is obtained. 相似文献
20.
When queueing models are used for performance analysis of some stochastic system, it is usually assumed that the system is in steady-state. Whether or not this is a realistic assumption depends on the speed at which the system tends to its steady-state. A characterization of this speed is known in the queueing literature as relaxation time.The discrete D/G/1 queue has a wide range of applications. We derive relaxation time asymptotics for the discrete D/G/1 queue in a purely analytical way, mostly relying on the saddle point method. We present a simple and useful approximate upper bound which is sharp in case the load on the system is not very high. A sharpening of this upper bound, which involves the complementary error function, is then developed and this covers both the cases of low and high loads.For the discrete D/G/1 queue, the stationary waiting time distribution can be expressed in terms of infinite series that follow from Spitzer’s identity. These series involve convolutions of the probability distribution of a discrete random variable, which makes them suitable for computation. For practical purposes, though, the infinite series should be truncated. The relaxation time asymptotics can be applied to determine an appropriate truncation level based on a sharp estimate of the error caused by truncating.This revised version was published online in June 2005 with corrected coverdate 相似文献