The Experts below are selected from a list of 246 Experts worldwide ranked by ideXlab platform
János Sztrik - One of the best experts on this subject based on the ideXlab platform.
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Performance Analysis and Statistical Modeling of the Single-Server Non-reliable Retrial Queueing System with a Threshold-Based Recovery
Communications in Computer and Information Science, 2015Co-Authors: Dmitry Efrosinin, János SztrikAbstract:In this paper we study a single-Server Markovian retrial queueing system with non-reliable Server and threshold-based recovery policy. The arrived customer finding a Free Server either gets service immediately or joins a retrial queue. The customer at the head of the retrial queue is allowed to retry for service. When the Server is busy, it is subject to breakdowns. In a failed state the Server can be repaired with respect to the threshold policy: the repair starts when the number of customers in the system reaches a fixed threshold level. Using a matrix-analytic approach we perform a stationary analysis of the system. The optimization problem with respect to the average cost criterion is studied. We derive expressions for the Laplace transforms of the waiting time. The problem of estimation and confidence interval construction for the fully observable system is studied as well.
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MODELING FINITE-SOURCE RETRIAL QUEUEING SYSTEMS WITH UNRELIABLE HETEROGENEOUS ServerS AND DIFFERENT SERVICE POLICIES USING MOSEL
2007Co-Authors: Patrick Ẅuchner, Janos Roszik, Gunter Bolch, Hermann De Meer, János SztrikAbstract:This paper deals with the performance analysis of multiple Server retrial queueing systems with a finite number of homogeneous sources of calls, where the heterogeneous Servers are subject to random breakdowns and repairs. The requests are serviced according to Random Selection and Fastest Free Server disciplines. The novelty of this investigation is the introduction of different service rates and different service policies together with the unreliability of the Servers, which has essential influence on the performance of the system, and thus it plays an important role in practical modeling of computer and communication systems. All random variables involved in the model construction are assumed to be exponentially distributed and independent of each other. The main steady-state performability measures are derived, and several numerical calculations are carried out by the help of the MOSEL tool (Modeling, Specification and Evaluation Language) under different service disciplines. The numerical results are graphically displayed to illustrate the effect of failure rates on the mean response time and on the overall system’s utilization.
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STOCHASTIC ANALYSIS OF CONTROLLED RETRIAL QUEUES WITH HETEROGENEOUS ServerS AND CONSTANT RETRIAL RATE 1
2006Co-Authors: Johannes Kepler, János SztrikAbstract:In this paper we analyse a controlled retrial queue with two exponential heterogeneous Servers in which the time between two successive repeated attempts is independent of the number of customers applying for the service. The customers upon arrival are queued in the orbit or enters service area according to the control policy. This system is analysed as controlled quasi-birth-and-death (QBD) process. It is showed that the optimal control policy is of threshold and monotone type. We propose the value iteration algorithm for the calculation of optimal threshold levels and perform the steady-state analysis using matrix-geometric approach. The main performance characteristics are calculated for the system under optimal threshold policy (OTP) and compared with the same characteristics for the model under scheduling threshold policy (STP) and other heuristic policies, e.g. the usage of the Fastest Free Server (FFS) or Random Server Selection (RSS).
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Modeling Finite-Source Retrial Queueing Systems with Heterogeneous Non-Reliable Servers by MOSEL
2005Co-Authors: Gunter Bolch, Janos Roszik, János SztrikAbstract:The aim of this paper is to analyze the performance of multiple Server retrial queueing systems with a finite number of homogeneous sources of calls, where the heterogeneous Servers are subject to random breakdowns and repairs. The requests are serviced according to Fastest Free Server ( FFS ) discipline.The novelty of this paper is the different service rates and non-reliability of the Servers, which has a very adverse influence on the performance of the system, thus it plays an important role in practical modeling of computer and communication systems. All random variables involved in the model construction are assumed to be exponentially distributed and independent of each other. The main performance and reliability measures are derived, and some numerical calculations are carried out by the help of the MOSEL ( Modeling, Specification and Evaluation Language ) tool. The numerical results are graphically displayed to illustrate the effect of the non-reliability of the Servers on the mean response time, on the overall system’s utilization and on the Servers’s utilization.
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Performance Modelling of Nonhomogeneous Unreliable MultiServer Systems Using MOSEL
Computers & Mathematics with Applications, 2003Co-Authors: Aymen I. Zreikat, G. Bolch, János SztrikAbstract:Abstract In this paper, we introduce a nonhomogeneous unreliable multiServer system with Markovian arrival, service, breakdown, and repair processes. First, we consider the case with only one queue and different Servers and the job is assigned to one Server. Then, we extend this model to more than one queue in which the jobs are assigned to different queues. We assume that our system has different Servers with different service times and a job is assigned to a Server using the following strategies: FFS (fastest Free Server) or random selection. FFS strategy means that the job is served by the fastest available Server, and if this Server is busy then the job goes to the next available Server and so on. In the random strategy, the job is served by one of the Free Servers which is chosen randomly. In our problem, we consider a general queuing system (M/M/n) with a finite number of jobs K in the whole system. Our system is unreliable; this means that we need to specify the parameters, mtbf and mttr (mean time between failures and mean time to repair), and we need to consider the possibility that a Server might be up or down at some point in time. The performance. modelling of this type, of system is done using the programming language MOSEL (Modelling Specification and Evaluation Language), which contains several constructs to describe the system, the results (performance parameters), and the graphical representation.
Wen Lea Pearn - One of the best experts on this subject based on the ideXlab platform.
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A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation
Optimization, 2013Co-Authors: Wen Lea PearnAbstract:In this study, we consider an M/M/c retrial queue with Bernoulli vacation under a single vacation policy. When an arrived customer finds a Free Server, the customer receives the service immediately; otherwise the customer would enter into an orbit. After the Server completes the service, the Server may go on a vacation or become idle (waiting for the next arriving, retrying customer). The retrial system is analysed as a quasi-birth-and-death process. The sufficient and necessary condition of system equilibrium is obtained. The formulae for computing the rate matrix and stationary probabilities are derived. The explicit close forms for system performance measures are developed. A cost model is constructed to determine the optimal values of the number of Servers, service rate, and vacation rate for minimizing the total expected cost per unit time. Numerical examples are given to demonstrate this optimization approach. The effects of various parameters in the cost model on system performance are investigated.
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Multi-Server retrial queue with second optional service: algorithmic computation and optimisation
International Journal of Systems Science, 2011Co-Authors: Wen Lea PearnAbstract:We consider an infinite-capacity M/M/c retrial queue with second optional service (SOS) channel. An arriving customer finds a Free Server would enter the service (namely, the first essential service, denoted by FES) immediately; otherwise, the customer enters into an orbit and starts generating requests for service in an exponentially distributed time interval until he finds a Free Server and begins receiving service. After the completion of FES, only some of them receive SOS. The retrial system is modelled by a quasi-birth-and-death process and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix-analytic approach. A cost model is derived to determine the optimal values of the number of Servers and the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimisation approach as well as the effect of various parameters on system performance measures.
Darrell D. E. Long - One of the best experts on this subject based on the ideXlab platform.
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Variable bandwidth broadcasting protocol for video-on-demand
Multimedia Computing and Networking 2003, 2003Co-Authors: Jehan-francois Paris, Darrell D. E. LongAbstract:We present the first broadcasting protocol that can alter the number of channels allocated to a given video without inconveniencing the viewer and without causing any temporary bandwidth surge. Our variable bandwidth broadcasting (VBB) protocol assigns to each video a minimum number of channels whose bandwidths are all equal to the video consumption rate. Additional channels can be assigned to the video at any time to reduce the customer waiting time or retaken to Free Server bandwidth. The cost of this additional flexibility is quite reasonable as the bandwidth requirements of our VBB fall between those of the fast broadcasting protocol and the new pagoda broadcasting protocol.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Srinivas R. Chakravarthy - One of the best experts on this subject based on the ideXlab platform.
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A queueing model for crowdsourcing
Journal of the Operational Research Society, 2017Co-Authors: Srinivas R. Chakravarthy, Alexander N. DudinAbstract:Crowdsourcing is getting popular after a number of industries such as food, consumer products, hotels, electronics, and other large retailers bought into this idea of serving customers. In this paper, we introduce a multi-Server queueing model in the context of crowdsourcing. We assume that two types, say, Type 1 and Type 2, of customers arrive to a c -Server queueing system. A Type 1 customer has to receive service by one of c Servers while a Type 2 customer may be served by a Type 1 customer who is available to act as a Server soon after getting a service or by one of c Servers. We assume that a Type 1 customer will be available for serving a Type 2 customer (provided there is at least one Type 2 customer waiting in the queue at the time of the service completion of that Type 1 customer) with probability $$p, 0 \le p \le 1$$ p , 0 ≤ p ≤ 1 . With probability $$q = 1 - p$$ q = 1 - p , a Type 1 customer will opt out of serving a Type 2 customer provided there is at least one Type 2 customer waiting in the system. Upon completion of a service a Free Server will offer service to a Type 1 customer on an FCFS basis; however, if there are no Type 1 customers waiting in the system, the Server will serve a Type 2 customer if there is one present in the queue. If a Type 1 customer decides to serve a Type 2 customer, for our analysis purposes that Type 2 customer will be removed from the system as Type 1 customer will leave the system with that Type 2 customer. Under the assumption of exponential services for both types of customers we study the model in steady state using matrix analytic methods and establish some results including explicit ones for the waiting time distributions. Some illustrative numerical examples are presented.
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Analysis of a multi-Server queueing model with vacations and optional secondary services
Mathematica Applicanda, 2014Co-Authors: Srinivas R. ChakravarthyAbstract:In this paper we study a multi-Server queueing model in which the customer arrive according to a Markovian arrival process. The customers may require, with a certain probability, an optional secondary service upon completion of a primary service. The secondary services are offered (in batches of varying size) when any of the following conditions holds good: (a) upon completion of a service a Free Server finds no primary customer waiting in the queue and there is at least one secondary customer (including possibly the primary customer becoming a secondary customer) waiting for service; (b) upon completion of a primary service, the customer requires a secondary service and at that time the number of customers needing a secondary service hits a pre-determined threshold value; (c) a Server returning from a vacation finds no primary customer but at least one secondary customer waiting. The Servers take vacation when there are no customers (either primary or secondary) waiting to receive service. The model is studied as a QBD-process using matrix-analytic methods and some illustrative examples arediscussed.
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Analysis of MAP/PH/c Retrial Queue with Phase Type Retrials – Simulation Approach
Communications in Computer and Information Science, 2013Co-Authors: Srinivas R. ChakravarthyAbstract:In this paper we study a multi-Server retrial queueing model in which customers arrive according to a Markovian arrival process (MAP) and the service times are assumed to be of phase type (PH-type). An arriving customer finding all Servers busy will enter into a (retrial) orbit of infinite size. The customers in orbit will try to capture a Free Server after a random amount of time which is assumed to be of PH-type. Thus, every customer in the orbit has his/her own phase type distribution before attempting to get into service. Due to the complexity of the model and lack of attention to such models in the literature, we study this via simulation. After validating our simulated results against known results (both exact and approximation) for some special cases, we illustrate how one can underestimate or overestimate some key system performance measures by incorrectly assuming the retrial times to be exponential.
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Analysis of a multi-Server retrial queue with search of customers from the orbit
Performance Evaluation, 2006Co-Authors: Srinivas R. Chakravarthy, Achyutha Krishnamoorthy, V. C. JoshuaAbstract:We consider a multi-Server retrial queueing model in which customers arrive according to a Markovian arrival process (MAP). An arriving customer finding a Free Server enters into service immediately; otherwise the customer enters into an orbit of infinite size. An orbiting customer competes for service by sending out signals at random times until a Free Server is captured. The inter-retrial times are exponentially distributed with intensity depending on the number of customers in the orbit. Upon completion of a service, with a certain probability the Server searches for an orbiting customer. Assuming the search time to be negligible, and the service and retrial times to be exponentially distributed, we perform the steady state analysis of the model using direct truncation and matrix-geometric approximation. Efficient algorithms for computing various steady state performance measures and illustrative numerical examples are presented.
Marcel F. Neuts - One of the best experts on this subject based on the ideXlab platform.
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Analysis of multiServer queues with constant retrial rate
European Journal of Operational Research, 2001Co-Authors: Jesús R. Artalejo, Antonio Gómez-corral, Marcel F. NeutsAbstract:Abstract We consider multiServer retrial queues in which the time between two successive repeated attempts is independent of the number of customers applying for service. We study a Markovian model where each arriving customer finding any Free Server either enters service or leaves the service area and joins a pool of unsatisfied customers called `orbit'. This system is analyzed as a quasi-birth-and-death (QBD) process and its main performance characteristics are efficiently computed.
