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1.
We consider a discrete-time single-server queueing model where arrivals are governed by a discrete Markovian arrival process (DMAP), which captures both burstiness and correlation in the interarrival times, and the service times and the vacation duration times are assumed to have a general phase-type distributions. The vacation policy is that of a working vacation policy where the server serves the customers at a lower rate during the vacation period as compared to the rate during the normal busy period. Various performance measures of this queueing system like the stationary queue length distribution, waiting time distribution and the distribution of regular busy period are derived. Through numerical experiments, certain insights are presented based on a comparison of the considered model with an equivalent model with independent arrivals, and the effect of the parameters on the performance measures of this model are analyzed. 相似文献
2.
This paper analyzes a single-server finite-buffer vacation (single and multiple) queue wherein the input process follows a discrete-time batch Markovian arrival process (D-BMAP). The service and vacation times are generally distributed and their durations are integral multiples of a slot duration. We obtain the state probabilities at service completion, vacation termination, arbitrary, and prearrival epochs. The loss probabilities of the first-, an arbitrary- and the last-customer in a batch, and other performance measures along with numerical aspects have been discussed. The analysis of actual waiting time of these customers in an accepted batch is also carried out. 相似文献
3.
4.
A problem of state feedback stabilization of discrete-time stochastic processes under Markovian switching and random diffusion (noise) is considered. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. Sufficient conditions based on linear matrix inequalities (LMI's) for stochastic stability is obtained. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results. 相似文献
5.
S. Chakravarthy 《商业与工业应用随机模型》1996,12(3):179-191
We consider a finite capacity queue with Markovian arrivals, in which the service rates are controlled by two pre-determined thresholds, M and N. The service rate is increased when the buffer size exceeds N and then brought back to normal service rate when the buffer size drops to M. The normal and fast service times are both assumed to be of phase type with representations (β, S), and β θS), respectively, where θ>1. For this queueing model, steady state analysis is performed. The server duration in normal as well as fast periods is shown to be of phase type. The departure process is modelled as a MAP and the parameter matrices of the MAP are identified. Efficient algorithms for computing system performance measures are presented. We also discuss an optimization problem and present an efficient algorithm for arriving at an optimal solution. Some numerical examples are discussed. 相似文献
6.
Peixia Gao Sabine Wittevrongel Joris Walraevens Herwig Bruneel 《Mathematical Methods of Operations Research》2008,67(2):269-284
In this paper, we study the behavior of a discrete-time multiserver buffer system with infinite buffer size. Packets arrive
at the system according to a two-state Markovian arrival process. The service times of the packets are assumed to be constant,
equal to multiple slots. The behavior of the system is analyzed by means of an analytical technique based on probability generating
functions (PGF’s). Explicit expressions are obtained for the PGF’s of the system contents and the packet delay. From these,
the mean values, the variances and the tail distributions of the system contents and the packet delay are calculated. Numerical
examples are given to show the influence of various model parameters on the system behavior. 相似文献
7.
We consider a batch arrival finite buffer single server queue with inter-batch arrival times are generally distributed and
arrivals occur in batches of random size. The service process is correlated and its structure is presented through Markovian
service process (MSP). The model is analyzed for two possible customer rejection strategies: partial batch rejection and total batch rejection
policy. We obtain steady-state distribution at pre-arrival and arbitrary epochs along with some important performance measures,
like probabilities of blocking the first, an arbitrary, and the last customer of a batch, average number of customers in the
system, and the mean waiting times in the system. Some numerical results have been presented graphically to show the effect
of model parameters on the performance measures. The model has potential application in the area of computer networks, telecommunication
systems, manufacturing system design, etc.
相似文献
8.
We consider a finite buffer batch service queueing system with multiple vacations wherein the input process is Markovian arrival
process (MAP). The server leaves for a vacation as soon as the system empties and is allowed to take repeated (multiple) vacations. The
service- and vacation- times are arbitrarily distributed. We obtain the queue length distributions at service completion,
vacation termination, departure, arbitrary and pre-arrival epochs. Finally, some performance measures such as loss probability,
average queue lengths are discussed. Computational procedure has been given when the service- and vacation- time distributions
are of phase type (PH-distribution). 相似文献
9.
We consider a discrete-time queueing system with a single deterministic server, heterogeneous Markovian arrivals and finite capacity. Most existing techniques model the queueing system using a direct bivariate Markov chain which requires a state space that grows rapidly as the number of customer types increases. In this paper, we define renewal cycles in terms of the input process and model the system occupancy level on each renewal cycle using a one-dimensional Markov chain. We derive the exact joint steady-state probability distribution of both states of input and system occupancy with a considerably reduced state space, which leads to the efficient calculation of overall/individual performance measures such as loss probability and average delay. 相似文献
10.
This paper deals with a batch service queue and multiple vacations. The system consists of a single server and a waiting room of finite capacity. Arrival of customers follows a Markovian arrival process (MAP). The server is unavailable for occasional intervals of time called vacations, and when it is available, customers are served in batches of maximum size ‘b’ with a minimum threshold value ‘a’. We obtain the queue length distributions at various epochs along with some key performance measures. Finally, some numerical results have been presented. 相似文献
11.
This paper proposes a unified matrix-analytic approach to characterize the output processes of general discrete-time lossless/lossy
queueing systems in which time is synchronized/slotted into fixed length intervals called slots. The arrival process can be
continuous- or discrete-time Markovian processes. It can be either renewal or non-renewal. The service of a customer commences
at the beginning of a slot, consumes a random number of slots, and completes at the end of a later slot. The service times
are independent and follow a common and general distribution. Systems with and without server vacations are both treated in
this paper. These queueing systems have potential applications in asynchronous transfer mode (ATM) networks, packet radio
networks, etc. Since the output process of a node in a queueing network becomes an input process to some node at the next
stage, the results of this paper can be used to facilitate end-to-end performance analysis which has attracted more and more
attention in the literature.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
12.
S. Chakravarthy 《Queueing Systems》1993,13(4):385-407
The finite capacity queues, GI/PH/1/N and PH/G/1/N, in which customers are served in groups of varying sizes were recently introduced and studied in detail by the author. In this paper we consider a finite capacity queue in which arrivals are governed by a particular Markov renewal process, called a Markovian arrival process (MAP). With general service times and with the same type of service rule, we study this finite capacity queueing model in detail by obtaining explicit expressions for (a) the steady-state queue length densities at arrivals, at departures and at arbitrary time points, (b) the probability distributions of the busy period and the idle period of the server and (c) the Laplace-Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. Efficient algorithmic procedures for computing the steady-state queue length densities and other system performance measures when services are of phase type are discussed. An illustrative numerical example is presented. 相似文献
13.
$H_{\infty}$ feedback controls based on discrete-time state observations for singular hybrid systems with nonhomogeneous Markovian jump
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In this paper, the $H_{\infty}$-control problem for singular Markovian jump systems (SMJSs) with variable transition rates by feedback controls based on discrete-time state observations is studied. The mode-dependent time-varying character of transition rates is supposed to be piecewise-constant. By designing a feedback controller based on discrete-time state observations, employing a stochastic Lyapunov-Krasovskii functional, and combining with the linear matrix inequalities (LMIs) technologies, sufficient conditions under the case of nonhomogeneous transition rates are developed such that the controlled system is regular, impulse free, and stochastically stable. Subsequently, the upper bound on the duration $\tau$ between two consecutive state observations and prescribed $H_{\infty}$ performance $\gamma$ are derived. Moreover, the achieved results can be easily checked by the Matlab LMI Tool Box. Finally, two numerical examples are presented to show the effectiveness of the proposed methods. 相似文献
14.
S. K. Samanta U. C. Gupta M. L. Chaudhry 《4OR: A Quarterly Journal of Operations Research》2009,7(4):337-361
This paper considers a single-server queueing model with finite and infinite buffers in which customers arrive according to
a discrete-time renewal process. The customers are served one at a time under discrete-time Markovian service process (D-MSP).
This service process is similar to the discrete-time Markovian arrival process (D-MAP), where arrivals are replaced with service
completions. Using the imbedded Markov chain technique and the matrix-geometric method, we obtain the system-length distribution
at a prearrival epoch. We also provide the steady-state system-length distribution at an arbitrary epoch by using the supplementary
variable technique and the classical argument based on renewal-theory. The analysis of actual-waiting-time (in the queue)
distribution (measured in slots) has also been investigated. Further, we derive the coefficient of correlation of the lagged
interdeparture intervals. Moreover, computational experiences with a variety of numerical results in the form of tables and
graphs are discussed. 相似文献
15.
A. D. Banik M. L. Chaudhry U. C. Gupta 《Methodology and Computing in Applied Probability》2008,10(4):559-575
We consider a finite-buffer single-server queue with renewal input where the service is provided in batches of random size
according to batch Markovian service process (BMSP). Steady-state distribution of number of customers in the system at pre-arrival and arbitrary epochs have been obtained along
with some important performance measures. The model has potential applications in the areas of computer networks, telecommunication
systems, and manufacturing systems, etc.
相似文献
16.
This paper deals with an BMAP/G/1 G-queues with second optional service and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process (BMAP) and Markovian arrival process (MAP), respectively. After completion of the essential service of a customer, it may go for a second phase of service. The arrival of a negative customer removes the customer being in service. The server leaves for a vacation as soon as the system empties and is allowed to take repeated (multiple) vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We obtain the mean of the busy period based on the renewal theory. 相似文献
17.
In this paper, we consider a single server queuing model with an infinite buffer in which customers arrive according to a batch Markovian arrival process (BMAP). The services are offered in two modes. In mode 1, the customers are served one at a time and in mode 2 customers are served in groups of varying sizes. Various costs for holding, service and switching are imposed. For a given hysteretic strategy, we derive an expression for the cost function from which an optimal hysteretic control can be obtained. Illustrative numerical examples are presented. 相似文献
18.
Analysis of Stop-and-Wait ARQ for a wireless channel 总被引:1,自引:0,他引:1
Stijn De Vuyst Krzysztof Tworus Sabine Wittevrongel Herwig Bruneel 《4OR: A Quarterly Journal of Operations Research》2009,7(1):61-78
In this paper, we study the behavior of the transmitter buffer of a system working under a Stop-and-Wait retransmission protocol.
The buffer at the transmitter side is modeled as a discrete-time infinite-capacity queue. The numbers of information packets
entering the buffer during consecutive slots are assumed to be independent and identically distributed random variables. The
packets are sent over an unreliable channel and transmission errors occur in a correlated manner. Specifically, the probability
of an erroneous transmission is modulated by a two-state Markov chain. An expression is derived for the probability generating
function of the buffer content. This expression is then used to derive several queue-length characteristics and the mean packet
delay. Numerical examples illustrate the strong effect of error correlation on the system performance. The obtained analytical
results are also compared with appropriate simulations.
相似文献
19.
In this article, we consider a single-server, finite-capacity queue with random bulk service rule where customers arrive according to a discrete-time Markovian arrival process (D-MAP). The model is denoted by D-MAP/G Y /1/M where server capacity (bulk size for service) is determined by a random variable Y at the starting point of services. A simple analysis of this model is given using the embedded Markov chain technique and the concept of the mean sojourn time of the phase of underlying Markov chain of D-MAP. A complete solution to the distribution of the number of customers in the D-MAP/G Y /1/M queue, some computational results, and performance measures such as the average number of customers in the queue and the loss probability are presented. 相似文献