Complex Queueing Systems Research Articles

Performance analysis and ANFIS computing of a Markovian queuing model with intermittently accessible server under a hybrid vacation policy

In this study, we investigate a heterogeneous queueing model with intermittent server availability, server catastrophes, and a hybrid vacation policy. Our focus is on a specific scenario: server 1 is always available, while server 2 may experience breakdowns or vacations, making it intermittently accessible. Using the matrix-geometric approach (MGA), we derive matrix-based expressions for the stationary probability distribution of the number of customers in the system and various system performance measures. Additionally, we evaluate the cost function per unit of time to determine optimal values for the system’s decision variables. Furthermore, we employ an adaptive neural fuzzy inference system (ANFIS) based on soft computing technology to compare and analyze the numerical results obtained. Through this comprehensive analysis, our study contributes to the understanding and optimization of this complex queueing system, attracting the attention of researchers in the field and offering practical insights for real-world applications.

Timed Petri Nets for Modeling and Performance Evaluation of a Priority Queueing System

The application of queueing theory is very broad. Examples include electronic communication systems and devices. New technologies, electronic communication systems, and devices are used by many modern organizations. However, this implies certain requirements and risks. The requirements are, first and foremost, reliability, which accounts for the complexity and interdependence of the system. On the other hand, the stochastic characteristics and complexity of these systems introduce risks related to the demands of reliability control, transmission quality, availability, and security. The research conducted so far is concerned with relatively simple queueing models that require certain assumptions to be made about the stochastic nature of the event stream. This is because complex queueing systems are very difficult to analyze using analytical methods. Hence, this paper attempts to use timed Petri nets in the modeling and performance evaluation of queueing systems belonging to the PQS (Priority Queueing System) group. IntServ and DiffServ architectures are discussed, as well as queueing systems used in quality-of-service assurance. A weighted PQS that eliminates the possibility of blocking lower-priority traffic is investigated. Based on a Petri model, the performance characteristics of the studied system are obtained. The impact of data generation on the system performance was analyzed, showing that temporal Petri nets can be effectively used in the modeling and performance evaluation of PQS systems.

Improving service efficiency and throughput of cardiac surgery patients using Monte Carlo simulation: a queueing setting.

Bed occupancy rate (BOR) is important for healthcare policymakers. Studies showed the necessity of using simulation approach when encountering complex real-world problems to plan the optimal use of resources and improve the quality of services. So, the aim of the present study is to estimate average length of stay (LOS), BOR, bed blocking probability (BBP), and throughput of patients in a cardiac surgery department (CSD) using simulation models. We studied the behavior of a CSD as a complex queueing system at the Farshchian Hospital. In the queueing model, customers were patients and servers were beds in intensive care unit (ICU) and post-operative ward (POW). A computer program based on the Monte Carlo simulation, using Python software, was developed to evaluate the behavior of the system under different number of beds in ICU and POW. The queueing simulation study showed that, for a fixed number of beds in ICU, BOR in POW decreases as the number of beds in POW increases and LOS in ICU increases as the number of beds in POW decreases. Also, based on the available data, the throughput of patients in the CSD during 800days was 1999 patients. Whereas, the simulation results showed that, 2839 patients can be operated in the same period. The results of the simulation study clearly demonstrated the behavior of the CSD; so, it must be mentioned, hospital administrators should design an efficient plan to increase BOR and throughput of patients in the future.

An Algorithm for Asymptotic Mean and Variance for Markov Renewal Process of M/G/1 Type with Finite Level

The Markov renewal process (MRP) of M/G/1 type has been used for modeling many complex queueing systems with correlated arrivals and the special types of transitions of the MRP process corresponds to the departures from the queueing system. It can be seen from the central limit theorem for regenerative process that the distribution of the number of transitions of MRP is asymptotically normal. Thus, the asymptotic mean and variance of the number of transitions of MRP can be used to estimate the number of departures in the queueing system modelled by MRP. The aim of this paper is to present an algorithm for computing the asymptotic mean and variance for the number of level-down-transitions in a Markov renewal process of M/G/1 type with finite level. The results are applied to the queueing system with finite buffer and correlated arrivals.

Performance analysis of non-exhaustive wireless sensor networks based on queueing theory

An operation mechanism of wireless sensor networks with non-exhaustive service, multiple adaptive sleep and wake-up strategies is presented on the basis of the queueing theory. The operation mechanism is proposed to dominate the workload of the necessary topology maintenance and reduce the energy consumption. The wireless sensor networks are modelled as a complex discrete-time queueing system. We derive the probability generating functions of the number of the data packets, the access delay, and we obtain the expressions of the mean number of the data packets, the mean response time, the utilisation rate and the throughput, etc. The sensitivity analyses of the performance measures are presented by the numerical experiments. Furthermore, the mathematical analyses are made on the energy consumption. Nash equilibrium and the social optimisation strategies are analysed in detail on the utility by using game theory.

Characterizations of random walks on random lattices and their ramifications

We analyze the behavior of a particle moving along a d-dimensional lattice and representing a “doubly stochastic” random walk. Unlike the classical random walk, the lattice is randomly generated upon particle’s landing at a node. At any time, the particle is enclosed in a rectangular cylinder (i.e., with a bounded a-dimensional rectangle Ra at its base) it attempts to escape. Thus, the particle moves from one node to another at random epochs of time and, with some probability, leaves The particle may jump arbitrarily far beyond the boundary at its passage time. Furthermore, the particle’s location is not assumed to be known in real time, but only upon certain random epochs Of a key interest is the location of the particle at any time, where is the linear interpolation of particle’s positions at times τn’s. If denotes the first observed escape time (virtual first passage time), where we target the joint characteristic function of and itself, where or in tractable forms, thereby attempting to enhance as much as possible the probabilistic data lost due to the crudeness of the observations and to couple and with deterministic time intervals Among various applications, we discuss and treat antagonistic games of two active and several passive players as well as situations that occur in complex queueing systems.

A simulation-based heuristic that promotes business profit while increasing the perceived quality of service industries

This paper tackles the problem of minimising the direct server costs of complex multiple-server queueing systems while improving the quality perceived by customers. The problem is solved by finding the server roster, defined as the allocation of active individual servers in each time interval of the working day. As no closed solution is available at this time, it was obtained by simulation modelling. The complex queueing system was solved by a simulation-based heuristic that includes the dynamic arrivals, entity reneging and/or balking, multi-servicing, and the individual service-time distributions of servers. The distributions of the random variables of single or multiple-branch businesses were identified by sampling procedures for multiple company-branch deployment. The beneficial financial impact of the proposed solution is confirmed in numerical real-life banking scenarios. The quality perceived by customers (evaluated through the expected queueing time) was also improved. Finally, additional insights that might improve the system performance are highlighted.

Fluctuation analysis in queues with several operational modes and priority customers

We analyze a complex queueing system with a single server operating in three different modes and dependent on circumstances, servicing two different queues simultaneously. There are different switching policies that specify when the server takes one or two queues. Main techniques are based on fluctuation analysis. One of the objectives is to model processes that occur in software, computer, and electrical engineering, and to argue that methods of fluctuation theory produce closed form functionals.

Performance analysis of a complex queueing system with vacations in random environment

This article studies a complex queueing system with vacations in a multi-phase random environment. When the system is in operative phase i, i=1,2,…,n, customers are served one by one. Whenever the ...

Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue

If the number of customers in a queueing system as a function of time has a proper limiting steady-state distribution, then that steady-state distribution can be estimated from system data by fitting a general stationary birth-and-death (BD) process model to the data and solving for its steady-state distribution using the familiar local-balance steady-state equation for BD processes, even if the actual process is not a BD process. We show that this indirect way to estimate the steady-state distribution can be effective for periodic queues, because the fitted birth and death rates often have special structure allowing them to be estimated efficiently by fitting parametric functions with only a few parameters, for example, 2. We focus on the multiserver Mt/GI/s queue with a nonhomogeneous Poisson arrival process having a periodic time-varying rate function. We establish properties of its steady-state distribution and fitted BD rates. We also show that the fitted BD rates can be a useful diagnostic tool to see if an Mt/GI/s model is appropriate for a complex queueing system. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 664–685, 2015

Comments on: Queueing models for the analysis of communication systems

Over the last 30 years, Dr. Bruneel’s team has produced a continuous stream of high-quality papers, which focus on the use of generating functions in the analysis of complex queueing systems that arise in communication networks.

Exact Simulation of Non-Stationary Reflected Brownian Motion

This paper develops the first method for the exact simulation of reflected Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The running time of generating exact samples of non-stationary RBM at any time t is uniformly bounded. The method can be used as a guide for planning simulations of complex queueing systems with non-stationary arrival rates and/or service time.

Maximum entropy approach for batch-arrival queue under [formula omitted] policy with an un-reliable server and single vacation

We consider the M [ x ] / G / 1 queueing system, in which the server operates N policy and a single vacation. As soon as the system becomes empty the server leaves for a vacation of random length V . When he returns from the vacation and the system size is greater than or equal to a threshold value N , he starts to serve the waiting customers. If he finds fewer customers than N . he waits in the system until the system size reaches or exceeds N . The server is subject to breakdowns according to a Poisson process and his repair time obeys an arbitrary distribution. We use maximum entropy principle to derive the approximate formulas for the steady-state probability distributions of the queue length. We perform a comparative analysis between the approximate results with established exact results for various batch size, vacation time, service time and repair time distributions. We demonstrate that the maximum entropy approach is efficient enough for practical purpose and is a feasible method for approximating the solution of complex queueing systems.

Optimal Pricing That Coordinates Queues with Customer-Chosen Service Requirements

This article considers the problem of coordinating the admission rates and service requirements of a multiclass queue when these decisions are made on a decentralized basis. The customer classes are characterized by different demand patterns, delay costs, and service costs. Customers make individual decisions on whether to join the queue and, if so, their service requirements. Their class identities and service requirements are private information not known to the system manager. We develop a two-stage decision framework to analyze the problem and characterize the optimal admission rates and service requirements under both centralized and decentralized assumptions. We distinguish admission and service externality costs that lead to suboptimal performance under decentralized control. For a given service discipline, we derive optimal class-specific pricing schemes that can coordinate the system when only service requirements but not class identities are unobservable. When customer class identities are also unobservable, we consider two common service disciplines that offer undifferentiated service: processor sharing and first-come-first-served. Based on the general framework, for the M/G/s processor sharing queue, we show that a single variable fee (payment per unit of time in the system) can induce the optimal admission rates and service requirements for all customer classes. For the M/G/1 first-come-first-served queue, we show that a single pricing scheme that is quadratic in time in service can induce the optimal admission rates and service requirements for all customer classes. Our result demonstrates that, under suitable conditions, simple and undifferentiated pricing can coordinate complex queueing systems with heterogeneous customer classes.

Efficient data allocation for frequency domain experiments

Frequency domain experiments are efficient screening procedures for identifying important factors in simulation models. An empirical investigation involving a simple autoregressive system and a complex queueing system shows that allocating data unequally among the signal and noise runs may be more effective when the total data collection effort is limited.

Effective bandwidth and fast simulation of ATM intree networks

We consider the efficient estimation, via simulation, of very low buffer overflow probabilities in certain acyclic ATM queueing networks. We apply the theory of effective bandwidths and Markov additive processes to derive an asymptotically optimal simulation scheme for estimating such probabilities for a single queue with multiple independent sources, each of which may be either a Markov modulated process or an autoregressive process. This result extends earlier work on queues with either independent arrivals or with a single Markov modulated arrival source. The results are the extended to estimating loss probabilities for intree networks of such queues. Experimental results show that the method can provide many orders of magnitude reduction in variance in complex queueing systems that are not amenable to analysis.

Solution to complex queueing systems

In this paper, some very useful and applicable ideas are presented to facilitate solving complex problems in Queueing Theory. It is demonstrated how a spreadsheet can be used to solve problems which many practitioners find very intimidating. To this end an algorithm is presented which is particularly designed for easy implementation in a spreadsheet. A template is provided illustrating the implementation of the algorithm. The use of the template is demonstrated in various queueing applications.

Optimal design of a multiservice system: The line-penalty problem

This paper deals with the problem of optimally designing a complex queueing system in presence of some constraints. The system is constituted by a set of M/M/1 queueing (sub-)systems, sharing the same scarce resources, but otherwise running independently. The objective is to minimize an inefficiency index, defined as the maximum expected line-penalty among the subsystems. The service rates are the decision variables. Different special problems, admitting the same general formulation, are illustrated.

Error analysis for regenerative queueing estimators with special reference to gradient estimators via likelihood ratio

The performance of telecommunications systems is typically estimated (either analytically or by simulation) via queueing theoretic models. The gradient of the expected performance with respect to the various parameters (such as arrival rate or service rate) is very important as it not only measures the sensitivity to change, but is also needed for the solution of optimization problems. While the estimator for the expected performance is the sample mean of the simulation experiment, there are several possibilities for the estimator of the gradient. They include the obvious finite difference approximation, but also other recently advocated techniques, such as estimators derived from likelihood ratio transformations or from infinitesimal perturbations. A major problem in deciding upon which estimator to use and in planning the length of the simulation has been the scarcity of analytical error calculations for estimators of queueing models. It is this question that we answer in this paper for the waiting time moments (of arbitrary order) of theM / G / 1 queue by using the queueing analysis technique developed by Shalmon. We present formulas for the error variance of the estimators of expectation and of its gradient as a function of the simulation length; at arbitrary traffic intensity the formulas are recursive, while the heavy traffic approximations are explicit and of very simple form. For the gradient of the mean waiting time with respect to the arrival (or service) rate, and at 1 percent relative precision, the heavy traffic formulas show that the likelihood ratio estimator for the gradient reduces the length of the simulation required by the finite difference estimator by about one order of magnitude; further increasing the relative precision by a factor increases the reduction advantage by the same factor. At any relative precision, it exceeds the length of the simulation required for the estimation of the mean with the same relative precision by about one order of magnitude. While strictly true for theM / G / 1 queue, the formulas can also be used as guidelines in the planning of queueing simulations and of stochastic optimizations of complex queueing systems, particularly those with Poisson arivals.

The derivation of invariance relations in complex queueing systems with stationary inputs

We discuss a method of obtaining invariance relations in complex systems by using the theory of point processes. New formulae are given for obtaining them generally, and in particular in many-stage models such as tandem and network queues. The formulae are shown to be useful by applications to a many-server queue and a tandem queue. Stochastic inequalities in a tandem queue are also discussed using the invariance relations obtained.