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13
Equivalence, Reversibility, Symmetry and Concavity Properties in ForkJoin Queueing Networks with Blocking
, 1993
"... In this paper we study quantitative as well as qualitative properties of ForkJoin Queueing Networks with Blocking (FJQN/B's). Specifically, we prove results regarding the equivalence of the behavior of a FJQN/B and that of its duals and a strongly connected marked graph. In addition, we obt ..."
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In this paper we study quantitative as well as qualitative properties of ForkJoin Queueing Networks with Blocking (FJQN/B's). Specifically, we prove results regarding the equivalence of the behavior of a FJQN/B and that of its duals and a strongly connected marked graph. In addition, we obtain general conditions that must be satisfied by the service times to guarantee the existence of a long term throughput and its independence on the initial configuration. We also establish conditions under which the reverse of a FJQN/B has the same throughput as the original network. By combining the equivalence result for duals and the reversibility result, we establish a symmetry property for the throughput of a FJQN/B. Last, we establish that the throughput is a concave function of the buffer sizes and the initial marking, provided that the service times are mutually independent random variables belonging to the class of PERT distributions that includes the Erlang distributions. This la...
A Survey on Solution Methods for Task Graph Models
, 1993
"... We give in this paper a survey on models developed in the literature using the concept of task graphs, focusing on solution techniques. Different types of task graphs are considered, from PERTS networks to random task graphs. Reviewed solution methods include exact computations and bounds. ..."
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Cited by 10 (4 self)
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We give in this paper a survey on models developed in the literature using the concept of task graphs, focusing on solution techniques. Different types of task graphs are considered, from PERTS networks to random task graphs. Reviewed solution methods include exact computations and bounds.
Cycle time of stochastic maxplus linear systems
 Electronic Journal of Probability
, 2008
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Bounds on the Tail Distributions of MarkovModulated Stochastic MaxPlus Systems
, 1995
"... In this paper we consider a particular class of linear systems under the maxplus algebra and derive exponential upper bounds for the tail distribution of each component of the state vector in the case of Markov modulated input sequences. Our results are then applied to tandem queues with infinite b ..."
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Cited by 1 (1 self)
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In this paper we consider a particular class of linear systems under the maxplus algebra and derive exponential upper bounds for the tail distribution of each component of the state vector in the case of Markov modulated input sequences. Our results are then applied to tandem queues with infinite buffers, Markov modulated arrivals and deterministic service times.
Railway Timetable Stability Analysis Using Stochastic MaxPlus Linear Systems
"... Stability and robustness of a railway timetable are essential properties for punctual and reliable operations. Timetable performance evaluation is therefore an important aspect in the timetable design process. In particular, the stability and recoverability properties of a timetable with respect to ..."
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Stability and robustness of a railway timetable are essential properties for punctual and reliable operations. Timetable performance evaluation is therefore an important aspect in the timetable design process. In particular, the stability and recoverability properties of a timetable with respect to daily process time variations must be well analysed. The timetable must be able to recover from primary delays due to stochastic process times and it must be robust against secondary delays due to train interactions. This paper presents a stability analysis approach based on stochastic maxplus linear system theory. Stochastic counterparts of wellestablished concepts from the deterministic maxplus stability analysis are proposed, like timetable stability and realizability. General probability distributions can be used to model the primary stochastic behaviour of process times, while delay propagation due to timetable and infrastructure constraints are computed from the stochastic recursive system equations. Recently developed powerful algorithms can be utilized to analyse and improve largescale stochastic systems, and to establish the amount of stochastic variations that a timetable can absorb without external control.
An Analytical Approach to the Performance Evaluation of MasterSlave Computational Models
, 1997
"... Many stochastic models and analysis techniques have been proposed in the literature during the last two decades for the performance evaluation of parallel and distributed systems. However few of them are directly applicable to practical systems which are generally too complex. In this paper we analy ..."
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Many stochastic models and analysis techniques have been proposed in the literature during the last two decades for the performance evaluation of parallel and distributed systems. However few of them are directly applicable to practical systems which are generally too complex. In this paper we analyze performances of the masterslave computational model, one of the most commonly used models in parallel and distributed computations. We propose a hybrid analytical approach by using techniques from the theories of both stochastic task graphs and queueing networks. We apply this method to the analysis of a computational chemistry application running on a Transputer based system. The proposed method turns out to be not only very efficient in time for large systems but also very accurate compared to measuring.
Using Stochastic Recursive Equations as a Tool for Modeling and Performance Evaluation of Parallel Processing Systems
"... This report presents the approach of stochastic recursive equations (SRE) for the modeling and performance analysis of parallel systems. The aim of the paper is twofold. Firstly, we show how performance measures of many parallel systems can be adequately described and obtained using stochastic recur ..."
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This report presents the approach of stochastic recursive equations (SRE) for the modeling and performance analysis of parallel systems. The aim of the paper is twofold. Firstly, we show how performance measures of many parallel systems can be adequately described and obtained using stochastic recursive equations. Secondly, we give an assesment on the capability of the SRE approach. 1 Introduction In this report, we present modeling and performance analysis of several parallel processing systems using the approach based on stochastic recursive equations (SRE). The aim of the paper is twofold. Firstly, we show how performance measures of many parallel systems can be adequately described and obtained using stochastic recursive equations. Secondly, we give an assesment on the capability of the SRE approach. The use of such equations for performance analysis of parallel systems appeared first in [7, 8, 9]. In this paper, we extend the class of equations studied there to cope with the syst...
Inventory Control for Supply Chains with Service Level Constraints: A Synergy between Large Deviations and Perturbation Analysis
, 2002
"... We consider a model of a supply chain consisting of n production facilities in tandem and producing a single product class. External demand is met from the finished goods inventory maintained in front of the most downstream facility (stage 1); unsatisfied demand is backlogged. We adopt a basestock ..."
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We consider a model of a supply chain consisting of n production facilities in tandem and producing a single product class. External demand is met from the finished goods inventory maintained in front of the most downstream facility (stage 1); unsatisfied demand is backlogged. We adopt a basestock production policy at each stage of the supply chain, according to which the facility at stage i produces if inventory falls below a certain level wi and idles otherwise. We seek to optimize the hedging vector w = (w1,..., wn) to minimize expected inventory costs at all stages subject to maintaining the stockout probability at stage 1 below a prescribed level (service level constraint). We make rather general modeling assumptions on demand and production processes that include autocorrelated stochastic processes. We solve this stochastic optimization problem by combining analytical (large deviations) and sample pathbased (perturbation analysis) techniques. We demonstrate that there is a natural synergy between these two approaches.
Duality and Equivalencies in Closed Tandem Queueing Networks
, 1993
"... Duality and Equivalencies in Closed Tandem Queueing Networks Equivalence relations between closed tandem queueing networks are established. Four types of models are under consideration: singleserver infinitecapacity buffer queues, infiniteserver queues with resequencing, singleserver unitcapaci ..."
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Duality and Equivalencies in Closed Tandem Queueing Networks Equivalence relations between closed tandem queueing networks are established. Four types of models are under consideration: singleserver infinitecapacity buffer queues, infiniteserver queues with resequencing, singleserver unitcapacity buffer queues with blocking before service, and singleserver unitcapacity buffer queues with blocking after service. Using a customer/server duality we show that in a network consisting of singleserver infinitecapacitybuffer queues, customerdependent service times and serverdependent service times yield equivalent performance characteristics. We further show that for closed tandem queueing networks, a system consisting of singleserver infinitecapacitybuffer queues (resp. infiniteserver queues with resequencing) and a system consisting of singleserverunitcapacitybuffer queues with blocking before service (resp. blocking after service) have equivalent performance behaviors. As applications of these equivalence properties, we obtain new results on the analysis of symmetric closed tandem networks, where all