Calculation of sensitivities of throughputs and realization probabilities in closed queueing networks with finite buffer capacities

Cao, Xi‐Ren

doi:10.2307/1427203

Cited by 5 publications

(4 citation statements)

References 14 publications

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“…The proof is similar to that for the Jackson networks (Cao (1987a(Cao ( ), (1988a(Cao ( ), and (1988c). In the following, we shall emphasize the specific features of the state-dependent networks.…”

Section: S Statistical Properties Of the Sample Path Sensitivitymentioning

confidence: 57%

“…However, since blocking may cause discontinuity in the sample performance function, Lemmas 5.1 and 5.2, and Theorems 5.1 and 5.2, do not hold for networks in which one server may block two or more servers simultaneously. The situation is the same as the load-dependent case discussed in Cao (1989).…”

Section: Discussionmentioning

confidence: 98%

“…The results were extended to multiclass queueing networks and networks with finite capacity buffers. It was shown that equations similar to Equation (1.1) do not hold for all these networks (Cao (1989), (1988b». Necessary and sufficient conditions for similar equations and examples illustrating the conditions were given in these papers.…”

Section: Tj Lji All Nmentioning

confidence: 99%

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Realization factors and sensitivity analysis of queueing networks with state-dependent service rates

Cao

1990

Advances in Applied Probability

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The paper studies the sensitivity of the throughput with respect to a mean service rate in a closed queueing network with exponentially distributed service requirements and state-dependent service rates. The study is based on perturbation analysis of queueing networks. A new concept, the realization factor of a perturbation, is introduced. The properties of realization factors are discussed, and a set of equations specifying the realization factors are derived. The elasticity of the steady state throughput with respect to a mean service rate equals the product of the steady state probability and the corresponding realization factor. This elasticity can be estimated by applying a perturbation analysis algorithm to a sample path of the system. The sample path elasticity of the throughput with respect to a mean service rate converges with probability 1 to the elasticity of the steady state throughput. The theory provides an analytical method of calculating the throughput sensitivity and justifies the application of perturbation analysis.

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Section: S Statistical Properties Of the Sample Path Sensitivitymentioning

confidence: 57%

Section: Discussionmentioning

confidence: 98%

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Realization factors and sensitivity analysis of queueing networks with state-dependent service rates

Cao

1990

Advances in Applied Probability

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“…For the purpose of analysis, we define a new quantity G ( n ) as below Note that G ( n ) quantifies the performance potential difference between neighboring states n and n − 1. According to the theory of perturbation analysis (PA) (Cao 1994, Ho and Cao 1991), G ( n ) is called the perturbation realization factor (PRF) which measures the effect on the average performance when the initial state is perturbed from n − 1 to n . For our job assignment problem (3), G ( n ) can be understood as the benefit of reducing the long‐run average cost due to a service accomplishment.…”

Section: Optimal Policy Structurementioning

confidence: 99%

A c/μ‐Rule for Job Assignment in Heterogeneous Group‐Server Queues

Xia

Zhang

2022

Production and Operations Management

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W e study a dynamic job assignment problem in queueing systems with one class of Poisson arrivals and K groups of heterogeneous servers. A scheduling policy prescribes the job assignment among servers in each group at every state n (number of jobs in the system). Our goal is to obtain the optimal policy to minimize the long-run average cost, which involves the increasingly convex holding cost for jobs and the operating cost for working servers. This problem has wide application scenarios in operations management, such as job scheduling in manufacturing systems, packet routing in communication systems, and staffing in service systems. We prove that the optimal policy has monotone structures and quasi bang-bang control forms. Specifically, we discover that the optimal policy is governed by the marginal cost rate c − μG(n), where c is the operating cost rate, μ is the service rate, and G(n) is called the perturbation realization factor at state n. Under the condition of scale economies which can be guaranteed by any increasingly concave operating cost in μ, we prove that the optimal policy obeys a so-called c/μ-rule: Servers with a smaller c/μ should be occupied by jobs with higher priority. Optimality of multi-threshold type policies is further proved when the c/μ-rule is applied. Our c/μ-rule in group-server queues can be viewed as a counterpart of the famous cμ-rule in polling queues, which both significantly reduce the complexity of optimization problems. By utilizing these optimality structures, we also develop computationalefficient algorithms to determine the optimal policy numerically. Simulation experiments demonstrate the good scalability and robustness of the c/μ-rule, which are important for managerial practice.

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Relations between performance potentials and infinitesimal realization factors in closed queueing networks

Yin

Dai

et al. 2002

Appl. Math. Chin. Univ.

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In this paper ,the concept of the infinitesimal realization factor is extended to the parameter-dependent performance functions in closed queueing networks. Then the concepts of re alization matrix (its elements are called realization factors) and performance potential are introduced, and the relations between infinitesimal realization factors and these two quantities are discussed. This provides a united framework for both IPA and non IPA approaches. Finally.another physical meaning of the service rate is given.

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Calculation of sensitivities of throughputs and realization probabilities in closed queueing networks with finite buffer capacities

Cited by 5 publications

References 14 publications

Realization factors and sensitivity analysis of queueing networks with state-dependent service rates

Realization factors and sensitivity analysis of queueing networks with state-dependent service rates

A c/μ‐Rule for Job Assignment in Heterogeneous Group‐Server Queues

Relations between performance potentials and infinitesimal realization factors in closed queueing networks

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