Solving Open Queueing Network Problem

2018 ◽  
Vol 6 (7) ◽  
pp. 116
Author(s):  
Aman Kumar Sinha ◽  
S. P. Varma
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Service Facility ◽  
Network Problem ◽  
Open Queueing Network

Queueing networks may be considered as a group of inter-connected nodes (say ) where each node represents a service facility of some kind with servers at the node ( ). We propose to apply 1st the method given by J. R. Jackson and then we would like to solve the same problem by the method of J. D. C. Little.

scholarly journals Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

OR Spectrum ◽  
2021 ◽  
Author(s):  
Sonja Otten ◽  
Ruslan Krenzler ◽  
Lin Xie ◽  
Hans Daduna ◽  
Karsten Kruse
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Arrival Rate ◽  
Second Step ◽  
Original Network ◽  
Theoretical Methods ◽  
Solution Approach ◽  
Open Queueing Networks ◽  
Open Queueing Network ◽  
Storage Area

AbstractWe consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

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).

Software for Queueing Analysis

2018 ◽  
pp. 255-291
Keyword(s):  
Queueing Networks ◽  
Discrete Event ◽  
Queueing Network ◽  
Queueing Analysis ◽  
Discrete Events ◽  
Technical Literature ◽  
Event Simulation ◽  
Statistical Program ◽  
Service Times ◽  
Waiting Lines

Chapter 8 gives a brief discussion of computer simulation for discrete events. The chapter lists software programs in the technical literature that outline programs for the simulation of discrete events, both of commercial origin and free programs. In addition to the lists submitted, the authors present specialized packages for analysis and simulation of waiting lines in the R language. Statistical considerations are presented, which must be taken into account when obtaining data from simulations in situations of waiting lines. Chapter 8 presents three packages of the statistical program R: the “queueing” analysis package provides versatile tools for analysis of birth- and death-based Markovian queueing models and single and multiclass product-form queueing networks; “simmer” package is a process-oriented and trajectory-based discrete-event simulation (DES) package for R; and, the purpose of the “queuecomputer” package is to calculate, deterministically, the outputs of a queueing network, given the arrival and service times of all the customers. It also uses simulation for the implementation of a method for the calculation of queues with arbitrary arrival and service times. For each theme, the authors show the use of the packages in R.

Realization probability in closed Jackson queueing networks and its application

1987 ◽  
Vol 19 (03) ◽  
pp. 708-738 ◽  
Author(s):  
X. R. Cao
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Queueing Networks ◽  
Sample Path ◽  
Queueing Network ◽  
Jackson Network ◽  
The Mean ◽  
Service Times ◽  
A New Technique ◽  
Number Of Customers

Perturbation analysis is a new technique which yields the sensitivities of system performance measures with respect to parameters based on one sample path of a system. This paper provides some theoretical analysis for this method. A new notion, the realization probability of a perturbation in a closed queueing network, is studied. The elasticity of the expected throughput in a closed Jackson network with respect to the mean service times can be expressed in terms of the steady-state probabilities and realization probabilities in a very simple way. The elasticity of the throughput with respect to the mean service times when the service distributions are perturbed to non-exponential distributions can also be obtained using these realization probabilities. It is proved that the sample elasticity of the throughput obtained by perturbation analysis converges to the elasticity of the expected throughput in steady-state both in mean and with probability 1 as the number of customers served goes to This justifies the existing algorithms based on perturbation analysis which efficiently provide the estimates of elasticities in practice.

scholarly journals Product forms based on backward traffic equations

1995 ◽  
Vol 32 (02) ◽  
pp. 508-518
Author(s):  
Richard J. Boucherie
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
New Product ◽  
Capacity Constraints ◽  
Product Form ◽  
New Form ◽  
Product Forms ◽  
Exact Product

This paper introduces a new form of local balance and the corresponding product-form results. It is shown that these new product-form results allow capacity constraints at the stations of a queueing network without reversibility assumptions and without special blocking protocols. In particular, exact product-form results for heavily loaded queueing networks are obtained.

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.

scholarly journals Cyclic queueing networks with subexponential service times

2004 ◽  
Vol 41 (03) ◽  
pp. 791-801
Author(s):  
H. Ayhan ◽  
Z. Palmowski ◽  
S. Schlegel
Keyword(s):  
Queueing Networks ◽  
Time Distribution ◽  
Waiting Times ◽  
Queueing Network ◽  
Service Time Distribution ◽  
Tail Behavior ◽  
Cycle Times ◽  
General Service Times ◽  
Service Times ◽  
General Service

For a K-stage cyclic queueing network with N customers and general service times, we provide bounds on the nth departure time from each stage. Furthermore, we analyze the asymptotic tail behavior of cycle times and waiting times given that at least one service-time distribution is subexponential.

Overall station balance and decomposability for non-Markovian queueing networks

1998 ◽  
Vol 30 (03) ◽  
pp. 870-887 ◽  
Author(s):  
D. Fakinos ◽  
A. Economou
Keyword(s):  
Queueing Networks ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Necessary And Sufficient Conditions ◽  
Jackson Type ◽  
Necessary And Sufficient ◽  
Markovian Queueing Networks

Introducing the concept of overall station balance which extends the notion of station balance to non-Markovian queueing networks, several necessary and sufficient conditions are given for overall station balance to hold. Next the concept of decomposability is introduced and it is related to overall station balance. A particular case corresponding to a Jackson-type queueing network is considered in some more detail.

Stochastic Monotonicities in Jackson Queueing Networks

1997 ◽  
Vol 11 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Torgny Lindvall
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Zero Point ◽  
Monotonicity Property ◽  
Stochastic Monotonicity ◽  
Property A ◽  
Jackson Network ◽  
Queueing Process ◽  
Network Process ◽  
Number Of Customers

When starting from 0, a standard M/M/k queueing process has a second-order stochastic monotonicity property of a strong kind: its increments are stochastically decreasing (the SDI property). A first attempt to generalize this to the Jackson queueing network fails. This gives us reason to reexamine the underlying theory for stochastic monotonicity of Markov processes starting from a zero-point, in order to find a condition on a function of a Jackson network process to have the SDI property. It turns out that the total number of customers at time t has the desired property, if the network is idle at time O. We use couplings in our analysis; they are also of value in the comparison of two networks with different parameters.

Sign in / Sign up

Export Citation Format

Share Document