Finite queueing modeling and optimization : a selected review

This review provides an overview of the queueing modeling issues and the related performance evaluation and optimization approaches framed in a joined manufacturing and product engineering. Such networks are represented as queueing networks. The performance of the queueing networks is evaluated using an advanced queueing network analyzer: the generalized expansion method. Secondly, different model approaches are described and optimized with regards to the key parameters in the network (e.g. buffer and server sizes, service rates, and so on.

Optimal routing in general finite multi-server queueing networks

The design of general finite multi-server queueing networks is a challenging problem that arises in many real-life situations, including computer networks, manufacturing systems, and telecommunication networks. In this paper, we examine the optimal routing problem in arbitrary configured acyclic queueing networks. The performance of the finite queueing network is evaluated with a known approximate performance evaluation method and the optimization is done by means of a heuristics based on the Powell algorithm. The proposed methodology is then applied to determine the optimal routing probability vector that maximizes the throughput of the queueing network. We show numerical results for some networks to quantify the quality of the routing vector approximations obtained

Buffer and throughput trade-offs in M/G/1/K queueing networks: A bi-criteria approach

The optimal design of real-life systems modeled as finite queueing networks is a difficult stochastic optimization problem. Besides being non-linear and including integer variables, different objectives often conflict with each other. For example, one conflicting pair of objectives includes first minimizing the overall number of buffers and then maximizing throughput. In this paper, we present an original methodology to solve a buffer allocation and throughput trade-off problem in single server general queueing networks. An approximation of the complete set of all best solutions, known as the Pareto optimal or non-inferior set, is derived by a special version of a multi-objective genetic algorithm (MOGA). The applied MOGA proves to be suitable for the stochastic trade-off problem. A comprehensive set of computational results attest to the efficiency and efficacy of the proposed methodology. We were able to show from a medium-sized mixed network that the squared coefficient of service time variation plays an important role in buffer allocation, which indicates the importance of using a general service model. Moreover, after the analysis of the solutions in the decision variable space, we confirm that the buffer allocation is highly dependent on the target throughput, which sometimes can be sacrificed in favor of using fewer of the usually expensive buffer spaces

Topological network design of general, finite, multi-server queueing networks

The topological network design of general service, finite waiting room, multi-server queueing networks is a complex optimization problem. Series, merge, and split topologies are examined using an approximation method to estimate the performance of these queueing networks and an iterative search methodology to find the optimal buffer allocation within the network. The coefficient of variation is shown to be a significant factor in the buffer allocation for multiple servers in uniform and bottleneck server networks. Extensive computational results are included to illustrate the symmetries and asymmetries in the buffer patterns which emerge from the series, merge, and splitting topologies

On the system optimum of traffic assignment in M/G/c/c state-dependent queueing networks

The classical Wardrop System Optimum assignment model assumes that the users will cooperate with each other in order to minimize the overall travel costs. The importance of the system optimum model lies on its well-recognized ability of producing solutions that correspond to the most efficient way of using the scarce resources represented by the street and road capacities. In this paper, we present a version of the system optimum model in which the travel costs incurred on each path come from M/G/c/c state-dependent queueing networks, a stochastic travel time estimation formula which takes into account congestion effects. A Differential Evolution algorithm is proposed to solve the model. We motivate this version of the problem in several ways and computational results show that the proposed approach is efficient

Traffic intensity estimation in finite markovian queueing systems

\u3cp\u3eIn many everyday situations in which a queue is formed, queueing models may play a key role. By using such models, which are idealizations of reality, accurate performance measures can be determined, such as traffic intensity (ρ), which is defined as the ratio between the arrival rate and the service rate. An intermediate step in the process includes the statistical estimation of the parameters of the proper model. In this study, we are interested in investigating the finite-sample behavior of some well-known methods for the estimation of ρ for single-server finite Markovian queues or, in Kendall notation, M/M/1/K queues, namely, the maximum likelihood estimator, Bayesian methods, and bootstrap corrections. We performed extensive simulations to verify the quality of the estimators for samples up to 200. The computational results show that accurate estimates in terms of the lowest mean squared errors can be obtained for a broad range of values in the parametric space by using the Jeffreys' prior. A numerical example is analyzed in detail, the limitations of the results are discussed, and notable topics to be further developed in this research area are presented.\u3c/p\u3