scholarly journals Variational inference for Markovian queueing networks

2021 ◽  
Vol 53 (3) ◽  
pp. 687-715
Author(s):  
Iker Perez ◽  
Giuliano Casale
Keyword(s):  
Queueing Networks ◽  
Stochastic Systems ◽  
Optimization Problems ◽  
Jump Processes ◽  
Conditional Density ◽  
Job Transitions ◽  
Full Independence ◽  
Service Rates ◽  
Routing Mechanism ◽  
Intractable Problem

AbstractQueueing networks are stochastic systems formed by interconnected resources routing and serving jobs. They induce jump processes with distinctive properties, and find widespread use in inferential tasks. Here, service rates for jobs and potential bottlenecks in the routing mechanism must be estimated from a reduced set of observations. However, this calls for the derivation of complex conditional density representations, over both the stochastic network trajectories and the rates, which is considered an intractable problem. Numerical simulation procedures designed for this purpose do not scale, because of high computational costs; furthermore, variational approaches relying on approximating measures and full independence assumptions are unsuitable. In this paper, we offer a probabilistic interpretation of variational methods applied to inference tasks with queueing networks, and show that approximating measure choices routinely used with jump processes yield ill-defined optimization problems. Yet we demonstrate that it is still possible to enable a variational inferential task, by considering a novel space expansion treatment over an analogous counting process for job transitions. We present and compare exemplary use cases with practical queueing networks, showing that our framework offers an efficient and improved alternative where existing variational or numerically intensive solutions fail.

scholarly journals Finite Queueing Modeling and Optimization: A Selected Review

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
F. R. B. Cruz ◽  
T. van Woensel
Keyword(s):  
Performance Evaluation ◽  
Queueing Networks ◽  
Queueing Network ◽  
Expansion Method ◽  
Network Analyzer ◽  
Modeling And Optimization ◽  
Product Engineering ◽  
Service Rates

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 regard to the key parameters in the network (e.g., buffer and server sizes, service rates, and so on).

scholarly journals Robust scheduling for flexible processing networks

2017 ◽  
Vol 49 (2) ◽  
pp. 603-628 ◽  
Author(s):  
Ramtin Pedarsani ◽  
Jean Walrand ◽  
Yuan Zhong
Keyword(s):  
Queueing Networks ◽  
Complex Structure ◽  
Job Flows ◽  
Heterogeneous Servers ◽  
Robust Scheduling ◽  
System Parameters ◽  
Balanced Allocation ◽  
Service Rates ◽  
Length Changes ◽  
Processing Networks

Abstract Modern processing networks often consist of heterogeneous servers with widely varying capabilities, and process job flows with complex structure and requirements. A major challenge in designing efficient scheduling policies in these networks is the lack of reliable estimates of system parameters, and an attractive approach for addressing this challenge is to design robust policies, i.e. policies that do not use system parameters such as arrival and/or service rates for making scheduling decisions. In this paper we propose a general framework for the design of robust policies. The main technical novelty is the use of a stochastic gradient projection method that reacts to queue-length changes in order to find a balanced allocation of service resources to incoming tasks. We illustrate our approach on two broad classes of processing systems, namely the flexible fork-join networks and the flexible queueing networks, and prove the rate stability of our proposed policies for these networks under nonrestrictive assumptions.

Optimal control of service rates in networks of queues

1987 ◽  
Vol 19 (1) ◽  
pp. 202-218 ◽  
Author(s):  
Richard R. Weber ◽  
Shaler Stidham
Keyword(s):  
Rate Control ◽  
Queueing Networks ◽  
Arrival Rate ◽  
Service Rate ◽  
Discounted Cost ◽  
Holding Costs ◽  
Optimal Service ◽  
Monotonicity Result ◽  
Service Rates ◽  
Number Of Customers

We prove a monotonicity result for the problem of optimal service rate control in certain queueing networks. Consider, as an illustrative example, a number of ·/M/1 queues which are arranged in a cycle with some number of customers moving around the cycle. A holding cost hi(xi) is charged for each unit of time that queue i contains xi customers, with hi being convex. As a function of the queue lengths the service rate at each queue i is to be chosen in the interval , where cost ci(μ) is charged for each unit of time that the service rate μis in effect at queue i. It is shown that the policy which minimizes the expected total discounted cost has a monotone structure: namely, that by moving one customer from queue i to the following queue, the optimal service rate in queue i is not increased and the optimal service rates elsewhere are not decreased. We prove a similar result for problems of optimal arrival rate and service rate control in general queueing networks. The results are extended to an average-cost measure, and an example is included to show that in general the assumption of convex holding costs may not be relaxed. A further example shows that the optimal policy may not be monotone unless the choice of possible service rates at each queue includes 0.

scholarly journals Throughput Maximization of Queueing Networks with Simultaneous Minimization of Service Rates and Buffers

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
F. R. B. Cruz ◽  
G. Kendall ◽  
L. While ◽  
A. R. Duarte ◽  
N. L. C. Brito
Keyword(s):  
Genetic Algorithm ◽  
Queueing Networks ◽  
Queueing Network ◽  
Efficient Solutions ◽  
Throughput Maximization ◽  
Service Rate ◽  
Multiobjective Genetic Algorithm ◽  
Conflicting Objectives ◽  
Service Rates ◽  
General Service

The throughput of an acyclic, general-service time queueing network was optimized, and the total number of buffers and the overall service rate was reduced. To satisfy these conflicting objectives, a multiobjective genetic algorithm was developed and employed. Thus, our method produced a set of efficient solutions for more than one objective in the objective function. A comprehensive set of computational experiments was conducted to determine the efficacy and efficiency of the proposed approach. Interesting insights obtained from the analysis of a complex network may assist practitioners in planning general-service queueing networks.

Some distributional approximations in Markovian queueing networks

1982 ◽  
Vol 14 (03) ◽  
pp. 654-671 ◽  
Author(s):  
T. C. Brown ◽  
P. K. Pollett
Keyword(s):  
Queueing Networks ◽  
Poisson Processes ◽  
Single Class ◽  
Open Network ◽  
State Dependent ◽  
Service Rates ◽  
Distributional Approximations ◽  
Closed Network ◽  
Poisson Approximations ◽  
Markovian Queueing Networks

We consider single-class Markovian queueing networks with state-dependent service rates (the immigration processes of Whittle (1968)). The distance of customer flows from Poisson processes is estimated in both the open and closed cases. The bounds on distances lead to simple criteria for good Poisson approximations. Using the bounds, we give an asymptotic, closed network version of the ‘loop criterion' of Melamed (1979) for an open network. Approximation of two or more flows by independent Poisson processes is also studied.

Some distributional approximations in Markovian queueing networks

1982 ◽  
Vol 14 (3) ◽  
pp. 654-671 ◽  
Author(s):  
T. C. Brown ◽  
P. K. Pollett
Keyword(s):  
Queueing Networks ◽  
Poisson Processes ◽  
Single Class ◽  
Open Network ◽  
State Dependent ◽  
Service Rates ◽  
Distributional Approximations ◽  
Closed Network ◽  
Poisson Approximations ◽  
Markovian Queueing Networks

We consider single-class Markovian queueing networks with state-dependent service rates (the immigration processes of Whittle (1968)). The distance of customer flows from Poisson processes is estimated in both the open and closed cases. The bounds on distances lead to simple criteria for good Poisson approximations. Using the bounds, we give an asymptotic, closed network version of the ‘loop criterion' of Melamed (1979) for an open network. Approximation of two or more flows by independent Poisson processes is also studied.

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