Queueing Systems – A Numerical Approach (original) (raw)

Calculation of delay characteristics for multiserver queues with constant service times

European Journal of Operational Research, 2009

We consider a discrete-time infinite-capacity queueing system with a general uncorrelated arrival process, constant-length service times of multiple slots, multiple servers and a first-come-first-served queueing discipline. Under the assumption that the queueing system can reach a steady state, we first establish a relationship between the steady-state probability distributions of the system content and the customer delay. Next, by means of this relationship, an explicit expression for the probability generating function of the customer delay is obtained from the known generating function of the system content, derived in previous work. In addition, several characteristics of the customer delay, namely the mean value, the variance and the tail distribution of the delay, are derived through some mathematical manipulations. The analysis is illustrated by means of some numerical examples.

THE ANALYSIS OF THE RESULTS OF SIMULATION MODELS OF LIMITED AND UNLIMITED QUEUING SERVICE SYSTEMS

The comparative analysis of the results of simulation models of limited and unlimited queuing service systems is reviewed. Here, when the restriction put on the time of presence of requests is violated, the loss of requests occurs. The analysis of possible situations leading to the loss in such systems is one of the important issues. These situations occur practically in service processes of different technical systems. An experiment was conducted; results were obtained and comparatively analyzed for both cases.

The-Application-of-Queuing-Analysis-in-modeling-Optimal-Service-level.pdf

Queues are common scenario faced in the modern day Banks and other financial Institutions. Queuing theory is the mathematical study of waiting lines; this can also be applicable queues in the banking system. This study examine the queuing system at Guarantee Trust Bank (GTB), putting into consideration the waiting time spend by Customers, Service time spend by a Customer and the average cost a customer loses while in queue and the service cost of each server in order to optimize the system. The First Come First Serve (FCFS) Multi-Server queuing model was used to model the queuing process. The waiting time was assumed to follow a Poisson distribution while the service rate follows an Exponential distribution. This study adopted a case study approach by randomly administering questionnaires, interviews and observation of the participants. The data were collected at the GTB cash deposit unit for four days period. The data collected were analyzed using TORA optimization window based software as well as standard queuing formula. The results of the analysis showed that the average queue length, waiting time of customer with a minimum Total Cost that utilize the system is by using five Servers against the present server level of Three Servers which incur a high total cost to both the Customers and the system.

Statistical techniques for a numerical evaluation of the proximity of and queueing systems

Computers & Mathematics with Applications, 2011

We study the strong stability of a G/M/1 queueing system after perturbation of the service times. We are interested in the determination of the proximity error between the corresponding service time distributions of G/G/1 and G/M/1 systems, the approximation error on the stationary distributions, and confidence intervals for the difference between the corresponding characteristics of the quoted systems in the stationary state, when the general distribution of service times G in the G/G/1 system is unknown and must be estimated by means of a nonparametric estimation method. We use the Student test to accept or reject the equality of the corresponding characteristics. The boundary effects are taken into account. Simulation studies are performed to support the results.

A NON LINEAR APPROACH TO QUEUEING SYSTEM MODELLING

2010

This paper seeks to establish queueing models that can help organizations to improve on their customer service within and outside their establishment. New Models were created using non linear regression analysis which is more convenient for the organizations to assess. It was found that The Coefficient of determination, R 2 value equals 1 and that the Degree of Correlation is 100% which indicates that 100% of the original uncertainty has been explained by the model.

Numerical method for the analysis of queuing models with priority jumps1

Cybernetics and Systems Analysis, 2013

An algorithmic approach to study queuing models with common finite and infinite buffer and jump priorities is developed. It is assumed that upon arrival of a low-priority call, one call of such kind can be transferred with some probability to the end of the queue of high-priority calls. The transition probability depends on the state of the queue of heterogeneous calls. The algorithms are proposed to calculate the quality of service metrics of such queuing models.

A model for waiting times for non-stationary queueing systems

Journal of Management and Science, 2016

Queueing models are stochastic models that represent the probability that a queueing system will be found in a particular configuration or state. Several interesting stationary queueing systems have been solved analytically; on the other hand, non-stationary queueing systems are relatively unexplored. The present study analyses the waiting times of a non-stationary M/M/1 queueing system using simulation methods.

Performance Analysis of A Queueing System with Server Arrival and Departure

ACM SIGMETRICS Performance Evaluation Review

In many systems, in order to fulfill demand (computing or other services) that varies over time, service capacities often change accordingly. In this paper, we analyze a simple two dimensional Markov chain model of a queueing system in which multiple servers can arrive to increase service capacity, and depart if a server has been idle for too long. It is well known that multi-dimensional Markov chains are in general difficult to analyze. Our focus is on an approximation method of stationary performance of the system via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the Poisson equation with a partial differential operator.

Modeling queues with simulation versus M/M/C models

Journal of Service Science Research, 2014

This paper examines the performance of single-queue service systems using a combination of computer simulation and M/M/C queuing models. Our results show that the accuracy of M/M/C models is significantly affected by the assumptions supporting the models. Managers should therefore exercise caution in using the M/M/C models for designing queuing systems when the models' assumptions are violated. Our results show that cost-centric and servicecentric firms should manage their queues differently. While cost-centric firms should target higher arrival load, single service session, and front-loaded arrival pattern for higher efficiency, service-centric firms should strive for lower arrival load, multiple short sessions and even arrival pattern for better service. In addition, both cost-centric and service-centric firms can consider pooling servers together and reducing the variability of inter-arrival and service times to improve both cost and service simultaneously.