Queueing Problems Research Articles

Queue balancing of load and expedition service in a cement industry in Brazil

The load and weight process in a cement industry is one of logistic step that shows the biggest time of occurrence, increasing the queues. This study aims to do a scenarios to solve this queue problem. This way, it pretends to find an better resources distribuition.

An Inexact Fuzzy-Queue Programming Model for Coupled Coal and Power Management

In this study, a coupled coal and power management model is developed based on an inexact fuzzy-queue programming method. The model is applied to a case study of coupled coal and power management system. The results indicate that the developed model can afford reasonable measures for solving coal-blending and coal-resources-allocation problems in coupled coal and power management system. It is useful for (a) standardizing coal supply, (b) improving efficiencies of the boilers, and (c) reducing emissions of air pollutants for meeting local air-quality targets. Potential risks associated with coal shortages and instability due to property variations from multiple sources can also be highly lowered through diversifying coal sources. Moreover, it can handle queue problems and multiple uncertainties exist in coupled coal and power management activities. Thus, it can help decision makers obtain optimal coal-blending schemes and coal-allocation patterns.

On establishing initial inventory levels in the rent-to-own industry: an empirical analysis

A theoretic model is developed to calculate the optimal inventory investment for a firm in the rent-to-own industry. This investment question is shown to be equivalent to a queueing problem and queueing technology is employed to fashion a solution. The initial inventory level is a critical decision which should be made to maximise expected profit. The decision is complicated by the fact that the arrival process of new customers, the total number of times that an item will be rented, and the length of time an item is kept by a customer are all random variables. Despite this, the model is able to provide closed-form solutions for various parameters, e.g., the probability that a potential customer will be lost due to product unavailability. A compelling feature of the current study is our access to a large and detailed transactional database. This is used to gain insight into actual contract usage and to numerically estimate the input parameters to our model. The resultant optimal inventory level is then compared against the actual levels providing a clear goodness-of-fit test for our overall approach.

A queue-based interval-fuzzy programming approach for electric-power systems planning

In this study, a queue-based interval-fuzzy electric-power system (QIF-ESP) model is developed through coupling fuzzy queue (FQ) theory with interval-parameter programming (IPP). QIF-ESP cannot only handle uncertainties that are presented in terms of fuzzy sets and interval numbers, but also reflect the effects of fuzzy queue on energy resources allocation and system cost. The QIF-EPS model is applied to a case study of planning a regional-scale electric-power system, where two FM/FM/1 (fuzzy exponential interarrival time, fuzzy exponential service time, and one server) queues are incorporated within the modeling framework. Interval solutions with fuzzy arrival and service rates have been generated, which result in different energy resources allocation patterns as well as changed waiting costs and system costs. Compared with the conventional optimization methods, the QIF-ESP model can effectively handle queue problems and multiple uncertainties exist in energy-related processes and activities. Moreover, consideration of queuing problem impacts in the optimization model can provide more useful information for decision makers and gain in-depth insights into the effects of queuing problems for electric-power systems under multiple uncertainties.

Under Utilization of Modern Health Facilities and the Practice of Alternative Medicine in Rural Areas of Rivers State

The study examined Utilisation of Health Care Facilities in some selected facilities in Rivers State. It sampled 400 respondents from 10 Local Government Areas of Rivers State. However, 366 copies of questionnaire representing (91.50% response rate) were used for the data analyses. The data analyses were achieved through the use of both descriptive and inferential statistical tools. The study revealed that socio-economic factors determine patronage of modern health facilities in the some selected local government areas in Rivers State. Major reasons provided by the respondents for not utilizing the basic health centres were presumed lack of equipment and drugs. The study revealed that the major effects of high cost of modern medicine on the people in rural areas include: shift to alternative medical treatments, low patronage to modern health facilities, spread of diseases, increase in self medication, ill health, proliferation of quacks in medical matters, increase rate of untimely death, recourse to superstitions and cultural heritage indulgence and reduced life span. The study also revealed that the facilities for modern health care services are largely concentrated in certain localities and this tends to make them inaccessible to most of the inhabitants in some parts of the local government areas. The study found that the main factors responsible for the non utilisation of modern health care facilities by the people in rural areas the problem of long queues, increase in poverty, stereo type beliefs/ culture, unemployment, inadequate information/ignorance and self-medication with traditional herbs. From the test of the hypotheses in this study it is evident and conclusive that: the poor health status of the people in rural communities is the result of under utilization of modern health care facilities in the areas; the use of alternative medicine due to low income is responsible for ineffective use of modern health facilities in rural areas and the non utilisation of modern health care facilities leads to underutilization of modern health facilities in rural areas. The study therefore, recommends that: Policy makers’ and all stakeholders’ attention should be drawn to improving the status and performance of the peripheral health facilities, improving the outlook image of the primary health facilities and making them environmental friendly.

Why do successful restaurants not raise their prices?

Becker (J Political Econ 99:1109–1116, 1991) addresses the problem of persistent queues at popular restaurants. He poses the question why such restaurants do not raise their prices, thus reducing the queues while expanding profits. He presents a solution based on the assumption that demand by a typical visitor to such a restaurant depends positively on the quantities demanded by others which could be so strong that the market demand curve slopes upward. For an equilibrium to emerge, Becker introduces a free lottery. We show that Becker’s lottery is based on assumptions which may hold in the case of spontaneously emerging queues, but not in situations like popular restaurants where consumers apply self-rationing. In both cases, however, every individual’s demand function, in addition to price, depends on effective demand rather than on aggregate demand. Using the forces underlying aggregated demand, we show that Becker’s solution leads to excess supply rather than excess demand. We use the all-or-nothing demand curve and the notion of patient consumer to show that a popular restaurant (and other firms facing persistent queues) sets a price such that equilibrium is achieved while long run demand is upheld.

On estimates of the spectrum of a linear operator

The paper is concerned with new approaches to the analysis of spectra of linear operators. New algorithms are proposed to calculate the coefficients of the minimal polynomial of a matrix; they are based on the well-known Krylov’s method, SSA decomposition, and the “Caterpillar” method of recurrent translation. The extension obtained is capable of dealing with matrices of infinite order; this has great value in solving queuing problems. Results from numerical experiments for matrices of various orders are given.

Resolution of Traffic Queue with Vision-Based Vehicle Detector

This paper proposes methods for solving problems of vehicle queues. The main purpose of the proposed system is to improve the detection accuracy when vehicle queues occur in traffic jams which appear frequently in real traffic conditions. For vision-based vehicle detectors, vehicle candidates will be detected from the foreground image, which is the subtraction between the current image and the background image. The procedure includes background extraction and segmentations of moving objects. However, when traffic jams happen, vehicle queues will occur. This phenomenon will heavily impact the detection accuracy. This paper presents methods for detecting queues, extracting occluded vehicles and splitting vehicles in queues. Finally, the experimental results show the proposed methods can improve the detection ratio effectively both in the urban and on highway.

Measure of performances of the strong stability method

In this paper, we propose a general approach to “measure” the performance of the strong stability method in queueing theory. This approach is based on discrete-event simulation and Student’s comparison method (Student’s test). We obtain the approximation precision in real situations (or at least, close to reality) which permits us to confirm the efficiency of the strong stability method for resolving concrete problems of queues. As an application, we choose two queueing models. The G/M/1 queue after perturbation of the service time distribution and the M/G/1 limit model for high retrial intensities, after perturbation of the retrial’s parameter.

Development of a Heuristics Model for Simplifying a Multi-Channel Queuing System

Queuing model has been discussed widely in literature. The structures of queuing systems are broadly divided into three namely; single, multi-channel, and mixed. Equations for solving these queuing problems vary in complexity. The most complex of them is the multi-channel queuing problem. A heuristically simplified equation based on relative comparison, using proportionality principle, of the measured effectiveness from the single and multi-channel models seems promising in solving this complex problem. In this study, six different queuing models were used from which five of them are single-channel systems while the balance is multi-channel. Equations for solving these models were identified based on their properties. Queuing models’ performance parameters were measured using relative proportionality principle from which complexity of multi-channel system was transformed to a simple linear relation of the form = . This showed that the performance obtained from single channel model has a linear relationship with corresponding to multi-channel, and is a factor which varies with the structure of queuing system. The model was tested with practical data collected on the arrival and departure of customers from a cocoa processing factory. The performances obtained based on average number of customers on line , average number of customers in the system , average waiting time in line and average waiting time in the system, under certain conditions showed no significant difference between using heuristics and analytical models.

On the Finite Capacity Shortest Queue Problem

We consider two parallel queues. There is one server tending to each queue and the capacity of each queue is K . The network is fed by a single Poisson arrival stream of rate λ, and the two servers are identical exponential servers working at rate µ. A new arrival is routed to the queue with the smaller number of customers. If both have the same number of customers then the arrival is routed randomly, with the probability of joining either queue being 1/2. If there are more than 2 K customers in the system, further arrivals are turned away and lost. We let ρ = λ/µ and take K →∞, and consider the cases ρ 2 and ρ − 2 = O ( K − 1 ). We shall obtain asymptotic approximations to the joint steady state distribution of finding m customers in the first queue and n in the second. The asymptotic approximations are shown to be quite accurate numerically. We shall identify precisely for what ranges of m and n can the finite capacity model be approximated by the infinite capacity one. We will also show that the marginal distribution of finding n customers in the second queue undergoes a transition when ρ = 4. Key words: Shortest queue problem; Finite capacity; Poisson arrival stream; Analytical approximations

The Interrelationship Between N-policy M/G/1/K and F-policy G/M/1/K Queues with Startup Time

This paper studies the interrelationship between the N-policy M/G/1/K queue and the F-policy G/M/1/K queue. The N- policy queuing problem investigates the most common issue of controlling service. The F- policy queuing problem deals with the most common issue of controlling arrivals. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to develop the solution algorithm for the N- policy M/G/1/K queue with startup time. We have demonstrated that the N-policy M/G/1/K queue with startup time has been effectively used to derive the solution algorithm to the F- policy G/M/1/K queue with startup time. The interrelationship between the N- policy and the F — policy queueing problems are illustrated analytically for 3-stage Erlang (service or interarrival) time distribution.

Event Scheduling in Simulation of Discrete Event Systems with Application on Queuing Systems.

Queuing theory and other of discrete and continuous event systems have theory aesthetic but the more assumptions which indepent these theories are not accurate as compared with real situation, also the queue problem is one of the most scientific problems that require simulation to analysi it. Because of that the aim of this research is to design event scheduling for simulation of discrete event systems and according to simulation time with application on simple and multiple queuing using MATLAB program (V.7.0)

Development of a Fuzzy-Queue-Based Interval Linear Programming Model for Municipal Solid Waste Management

Abstract In this study, a fuzzy-queue-based interval linear programming (FQ-ILP) model was first developed through introducing FQ model into an ILP framework. The FQ-ILP model can not only address system uncertainties with complex presentations, but also reflect the influence of FQ in decision-making problems. Moreover, it can be used for analyzing various policy scenarios that are associated with different waiting costs, fuzzy waiting times, and different operation costs. The method has been applied to a typical case study area for long-term municipal solid waste management planning. Interval solutions associated with fuzzy arrival rate, fuzzy service rate, and different waiting costs have been generated. They can be further used for generating decision alternatives and thus help waste managers to identify desired policies under various environmental, economic, and fuzzy queuing problems. Compared with the conventional optimization methods, the developed FQ-ILP model can more actually reflect the complex...

Solution for a retrial queueing problem in cellular networks with the Fractional Guard Channel policy

In this paper, we introduce a retrial queueing problem for wireless cellular networks applying the Fractional Guard Channel (FGC) admission control policy and propose a new algorithm to solve the retrial queue problem involving the FGC policy. A comparison between analytical and simulation results shows that our algorithm is accurate and fast to evaluate the performance of the system.

Control approach to Queue Theory

The rigid condition for simple queue problem is minimized by considering multiple channels through control approach. The result control problem is solved using Conventional Conjugate Gradient Method and the optimal system performance is obtained Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 371-378

Some first passage time problems for the shortest queue model

We consider the symmetric shortest queue (SQ) problem. Here we have a Poisson arrival stream of rate ? feeding two parallel queues, each having an exponential server that works at rate μ. An arrival joins the shorter of the two queues; if both are of equal length the arrival joins either with probability 1/2. We consider the first passage time until one of the queues reaches the value m 0, and also the time until both reach this level. We give explicit expressions for the first two first passage moments, conditioned on the initial queue lengths, and also the full first passage distribution. We also give some asymptotic results for m 0?? and various values of ?=?/μ.

Evaluating Service System Alternatives via a Computer Simulation‐enabled MCDM Framework

Decision makers in the service industry must effectively cope with queuing problems, service capacity optimization, service efficiency and service quality problems. This study proposes a computer simulation‐enabled MCDM framework that integrates computer simulation analysis, Taguchi method, expert opinion and multiple criteria decision making (MCDM) to assist decision makers in coping with decision problems. In this framework, Taguchi method is adopted to reduce the time required for the simulation experiment. Computer simulation analysis is adopted to obtain useful information for rapid decision‐making without interrupting actual production. MCDM is used to select the optimal alternative. The illustrative result is extremely promising.

A modified HOL priority scheduling discipline: Performance analysis

In this paper, we introduce and analyze a modified HOL (head-of-the-line) priority scheduling discipline. The modification is incorporated to cope with the so-called starvation problem of regular HOL priority queues. We consider a discrete-time single-server queueing system with two priority queues of infinite capacity and with the introduced priority scheme. We show that the use of probability generating functions is suitable for analyzing the system contents and the packet delay. Some performance measures (such as means and variances) of these stochastic quantities will be derived. Furthermore, approximate expressions of the tail probabilities are obtained from the probability generating functions, by means of the dominant-singularity method. These expressions, together with their characteristics, constitute one of the main contributions of this paper. Finally, the impact and significance of the m-HOL (modified HOL) priority scheduling on these performance measures is illustrated by some numerical examples.

Analysis of two queues in parallel with jockeying and restricted capacities

In this paper, we present two parallel queues with jockeying and restricted capacities. Each exponential server has its own queue, and jockeying among the queues is permitted. The capacity of each queue is restricted to L including the one being served. Customers arrive according to a Poisson process and on arrival; they join the shortest feasible queue. Moreover, if one queue is empty and in the other queue, more than one customer is waiting, then the customer who has to receive after the customer being served in that queue is transferred to the empty queue. This will prevent one server from being idle while the customers are waiting in the other queue. Using the matrix-analytical technique, we derive formulas in matrix form for the steady-state probabilities and formulas for other performance measures. Finally, we compare our new model with some of Markovian queueing systems such as Conolly’s model [B.W. Conolly, The autostrada queueing problems, J. Appl. Prob. 21 (1984) 394–403], M / M / 2 queue and two of independent M / M / 1 queues for the steady state solution.