共查询到20条相似文献,搜索用时 10 毫秒
1.
In this paper, we investigate the loss process in a finite-buffer queue with batch arrivals and total rejection discipline. In such a model, if the buffer has insufficient capacity to accept all the customers included in an arriving batch, the whole batch is blocked and lost. This scheme is especially useful in performance evaluation of buffering processes in IP (internet protocol) networks. The main result of this paper is a closed-form formula for the joint distribution of the length of the first lost series of batches and the time of the first loss. Moreover, the limiting distribution (as the buffer size grows to infinity) is shown. 相似文献
2.
An analysis is given of the state and first-come, first-served waiting time processes for a three stage queueing system with no waiting space between stages, but with limited space before the first. Although the basic processes are exponential, no detailed analysis in this generality appears to have been made before; the nearest analyses entail the simplifying assumption that the first stage is never empty. A sufficient condition is derived easily for equilibrium to exist and it can be asserted with virtual certainty that it is also necessary; the complexity of calculation has so far excluded a proper proof, though this is in principle a possibility.The objective is to provide a theoretical framework easily adaptable for a numerical assessment of system performance to be made. Some typical tables with comments are given. 相似文献
3.
N. K. Krivulin 《Vestnik St. Petersburg University: Mathematics》2007,40(4):279-286
A new technique of estimating the blocking probability in multiwave time division multiplexing networks is proposed. The technique is based on solution of combinatorial problems of calculating the number of compositions with bounded parts. 相似文献
4.
The model considered in this paper involves a tandem queue with two waiting lines, and as soon as the second waiting line
reaches a certain upper limit, the first line is blocked. Both lines have exponential servers, and arrivals are Poisson. The
objective is to determine the joint distribution of both lines in equilibrium. This joint distribution is found by using generalized
eigenvalues. Specifically, a simple formula involving the cotangent is derived. The periodicity of the cotangent is then used
to determine the location of the majority of the eigenvalues. Once all eigenvalues are found, the eigenvectors can be obtained
recursively. The method proposed has a lower computational complexity than all other known methods.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
We analyze a discrete-time network of queues. The unit element of the network is the 2 × 2 buffered switch, which we regard as a system of two queues working in parallel. We show how to transform transition probability information from the output of one switch, or network stage, to the input of the next one. This is used to carry out a Markov time series input model to predict mean queue length at every stage of the system. Another model considered is a renewal process time series model, which we use to find the mean queue length of the second stage of the network. Numerical simulations fall within the narrow band spanned by the two models. 相似文献
6.
Optimal order of servers in a tandem queue with general blocking 总被引:1,自引:0,他引:1
In this paper, using the bivariate characterizations of thereversed hazard rate ordering and thestochastic ordering, and thepairwise interchange argument, we characterize the best strategy for allocating servers in a tandem system controlled using thegeneral blocking or theproduction authorization card (PAC) schemes. We show that when there is no buffer space between the first (resp. the last) two servers, it is better to allocate the slower server to the first (resp. the last) stage. The result extends previous results to systems where the number of buffers at the interior stages may be greater than one and the blocking mechanism may be more general. In particular, our results apply to manufacturing blocking, kanban blocking, a variation of kanban blocking, and the integral control scheme previously studied in the literature. 相似文献
7.
V. ThangarajA. Santhakumaran 《Mathematical and Computer Modelling》1994,19(12):49-66
This paper focuses on the study of several random processes associated with M/G1 queue with instantaneous tri-route decision process. The stationary distribution of the output process is derived. Some particular queues with feedback and without feedback are also analysed. Some operating characteristics are studied for this queue. Optimum service rate is obtained. A numerical study is carried out to test the feasibility of the queueing model. 相似文献
8.
Nicholas Pippenger 《Random Structures and Algorithms》1991,2(2):121-149
We determine the limiting behavior of the blocking probability for spider-web networks, a class of crossbar switching networks proposed by Ikeno. We use a probabilistic model proposed by the author, in which the busy links always form disjoint routes through the network. We show that if the occupancy probability is below the threshold 2 - √2 = 0.5857…, then the blocking probability tends to zero, whereas above this threshold it tends to one. This provides a theoretical explanation for results observed empirically in simulations by Bassalygo, Neiman, and Vvedenskaya. 相似文献
9.
On the distribution of queue size in queueing problems 总被引:3,自引:0,他引:3
P. D. Finch 《Acta Mathematica Hungarica》1959,10(3-4):327-336
10.
In this paper, we develop two new general purpose recursive algorithms for the exact computation of blocking probabilities in multi-rate product-form circuit-switched networks with fixed routing. The first algorithm is a normalization constant approach based on the partition function of the state distribution. The second is a mean-value type of algorithm with a recursion cast in terms of blocking probabilities and conditional probabilities. The mean value recursion is derived from the normalization constant recursion. Both recursions are general purpose ones that do not depend on any specific network topology. The relative advantage of the mean-value algorithm is numerical stability, but this is obtained at the expense of an increase in computational costs.The results of section 2 were presented in part at the 7th ITC Seminar on Broadband Technologies, Morristown, NJ, October 1990.Supported in part by the National Science Foundation, Grant No. CCR-9015717. 相似文献
11.
《European Journal of Operational Research》1997,101(2):393-405
This paper is concerned with the determination of blocking probabilities in loss networks. In fact, our study consists of two parts. Primarily, we scale both arrival rates and link capacities, in order to derive rough asymptotical expressions. These expressions arise as the result of mathematical programming problems. Secondly, we develop a fast simulation technique to estimate the blocking probabilities. This technique is based on importance sampling, where the choice of the alternative probability model is closely related to the optimizing arguments of the above mentioned mathematical programming problem. Some examples show that huge gain of simulation effort can be achieved. 相似文献
12.
A novel approach for obtaining the response time in a discrete-time tandem-queue with blocking is presented. The approach constructs a Markov chain based on the age of the leading customer in the first queue. We also provide a stability condition and carry out several numerical examples. 相似文献
13.
In this paper an analysis of the output process from an M/M/1 queue where the arrival and service rates vary randomly is presented. The results include expressions for the mean, variance and distribution of the interdeparture interval, the joint density function of two successive interdeparture intervals and their correlation. An interesting feature of the results is that the moments of the interdeparture time are expressed in terms of the expected times to first and second departures from an arbitrary point in time. 相似文献
14.
15.
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
16.
Toshihisa Ozawa 《Queueing Systems》2006,53(4):203-211
We consider a general QBD process as defining a FIFO queue and obtain the stationary distribution of the sojourn time of a
customer in that queue as a matrix exponential distribution, which is identical to a phase-type distribution under a certain
condition. Since QBD processes include many queueing models where the arrival and service process are dependent, these results
form a substantial generalization of analogous results reported in the literature for queues such as the PH/PH/c queue. We
also discuss asymptotic properties of the sojourn time distribution through its matrix exponential form. 相似文献
17.
18.
19.
We introducegeneral starvation and consider cyclic networks withgeneral blocking and starvation (GBS). The mechanism of general blocking allows the server to process a limited number of jobs when the buffer downstream is full, and that of general starvation allows the server to perform a limited number of services in anticipation of jobs that are yet to arrive. The two main goals of this paper are to investigate how the throughput of cyclic GBS networks is affected by varying (1) the total number of jobsJ, and (2) the buffer allocationk=(k1..., km) subject to a fixed total buffer capacityK=k
1 +... + km. In particular, we obtain sufficient conditions for the throughput to be symmetric inJ and to be maximized whenJ=K/2. We also show that the equal buffer allocation is optimal under the two regimes of light or heavy usage. In order to establish these results, we obtain several intermediate structural properties of the throughput, using duality, reversibility, and concavity, which are of independent interest.Research supported in part by NSF Grant No. ECS-8919818. 相似文献
20.
The intuition while observing the economy of queueing systems, is that one’s motivation to join the system, decreases with
its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure
is the standard first-come first-served single server queue with Poisson arrivals. Customers commence service immediately
if upon their arrival the server is idle. Otherwise, they are informed if the queue is empty or not. Then, they have to decide
whether to join or not. We assume that the customers are homogeneous and when they consider whether to join or not, they assess
their queueing costs against their reward due to service completion. As the whereabouts of customers interact, we look for
the (possibly mixed) join/do not join Nash equilibrium strategy, a strategy that if adopted by all, then under the resulting
steady-state conditions, no one has any incentive not to follow it oneself. We show that when the queue is empty then depending
on the service distribution, both ‘avoid the crowd’ (ATC) and ‘follow the crowd’ (FTC) scenarios (as well as none-of-the-above)
are possible. When the queue is not empty, the situation is always that of ATC. Also, we show that under Nash equilibrium
it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than
it is when the queue is not empty.
This research was supported by The Israel Science Foundation Grant No. 237/02. 相似文献