scholarly journals Optimization Analysis of the N Policy M/G/1 Queue with Working Breakdowns

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 583
Author(s):  
Tseng-Chang Yen ◽  
Kuo-Hsiung Wang ◽  
Jia-Yu Chen
Keyword(s):  
Performance Measures ◽  
System Performance ◽  
Probability Generating Function ◽  
Optimization Method ◽  
Supplementary Variable ◽  
Optimization Analysis ◽  
Two Stage ◽  
Stability Constraint ◽  
Service Rates ◽  
The Stability

This paper deals with the N policy M/G/1 queue with working breakdowns. The supplementary variable and probability generating function techniques are implemented to develop the steady-state results. The stability condition of a stable queue, as well as several system performance measures, are also derived. A two-stage optimization method is employed to determine the optimal threshold N and the optimal joint values of two mean service rates until the stability constraint is satisfied. To demonstrate the effectiveness of two-stage optimization method, some numerical results are presented. Finally, we carry out sensitivity analysis for the expected cost function with numerical illustrations.

ANALYSIS OF A BULK QUEUE WITH FAST AND SLOW SERVICE RATES AND MULTIPLE VACATIONS

2005 ◽  
Vol 22 (02) ◽  
pp. 239-260 ◽  
Author(s):  
R. ARUMUGANATHAN ◽  
K. S. RAMASWAMI
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Queueing System ◽  
Cost Model ◽  
Probability Generating Function ◽  
Service Rate ◽  
Multiple Vacations ◽  
Bulk Queue ◽  
Service Rates ◽  
Number Of Customers

We analyze a Mx/G(a,b)/1 queueing system with fast and slow service rates and multiple vacations. The server does the service with a faster rate or a slower rate based on the queue length. At a service completion epoch (or) at a vacation completion epoch if the number of customers waiting in the queue is greater than or equal to N (N > b), then the service is rendered at a faster rate, otherwise with a slower service rate. After finishing a service, if the queue length is less than 'a' the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than 'a' he leaves for another vacation and so on until he finally finds atleast 'a' customers waiting for service. After a service (or) a vacation, if the server finds atleast 'a' customers waiting for service say ξ, then he serves a batch of min (ξ, b) customers, where b ≥ a. We derive the probability generating function of the queue size at an arbitrary time. Various performance measures are obtained. A cost model is discussed with a numerical solution.

scholarly journals Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period

2017 ◽  
Vol 5 (2) ◽  
pp. 176-192
Author(s):  
Shaojun Lan ◽  
Yinghui Tang
Keyword(s):  
Performance Measures ◽  
Generating Function ◽  
Discrete Time ◽  
Queueing System ◽  
Operating Cost ◽  
Probability Generating Function ◽  
Repair Process ◽  
Function Technique ◽  
Service Rate ◽  
The Stability

Abstract This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service. We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution. Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.

scholarly journals Queuing Analysis on Multiple Vacation Policies and Reneging

2019 ◽  
Vol 9 (1S4) ◽  
pp. 948-951
Keyword(s):  
Performance Measures ◽  
System Performance ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Queuing Analysis ◽  
Supplementary Variable Technique ◽  
Multiple Vacation ◽  
Markovian Queue

We study a non markovian queue which renders service to the customers. After the completion of service the server ought to go for the compulsory vacation stage by stage in succession. We consider one of the customer’s behaviors reneging to occur when the server’s vacation is extended. Using Supplementary variable technique the system performance measures is derived.

The anaerobic treatment of a ligno-cellulosic substrate offering little natural pH buffering capacity

1998 ◽  
Vol 38 (4-5) ◽  
pp. 29-35 ◽  
Author(s):  
C. J. Banks ◽  
P. N. Humphreys
Keyword(s):  
Ph Control ◽  
Anaerobic Treatment ◽  
Buffering Capacity ◽  
Single Stage ◽  
Stable Operation ◽  
Reactor Performance ◽  
Two Stage ◽  
Ph Buffering ◽  
Stage System ◽  
The Stability

The stability and operational performance of single stage digestion with and without liquor recycle and two stage digestion were assessed using a mixture of paper and wood as the digestion substrate. Attempts to maintain stable digestion in both single stage reactors were unsuccessful due to the inherently low natural buffering capacity exhibited; this resulted in a rapid souring of the reactor due to unbuffered volatile fatty acid (VFA) accumulation. The use of lime to control pH was unsatisfactory due to interference with the carbonate/bicarbonate equilibrium resulting in wide oscillations in the control parameter. The two stage system overcame the pH stability problems allowing stable operation for a period of 200 days without any requirement for pH control; this was attributed to the rapid flushing of VFA from the first stage reactor into the second stage, where efficient conversion to methane was established. Reactor performance was judged to be satisfactory with the breakdown of 53% of influent volatile solids. It was concluded that the reactor configuration of the two stage system offers the potential for the treatment of cellulosic wastes with a sub-optimal carbon to nitrogen ratio for conventional digestion.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

scholarly journals Approximate performance measures for a single station two-stage reneging queue

2021 ◽  
Vol 49 (2) ◽  
pp. 212-217
Author(s):  
Katsunobu Sasanuma ◽  
Alan Scheller-Wolf
Keyword(s):  
Performance Measures ◽  
Two Stage ◽  
Single Station

scholarly journals Stability of a one-dimensional morphoelastic model for post-burn contraction

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Ginger Egberts ◽  
Fred Vermolen ◽  
Paul van Zuijlen
Keyword(s):  
Wound Healing ◽  
Residual Stresses ◽  
Truncation Error ◽  
Signaling Molecules ◽  
Discrete Problem ◽  
One Dimensional ◽  
Stability Constraint ◽  
Biological Interpretation ◽  
The Stability ◽  
The One

AbstractTo deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

scholarly journals A Two-Stage Mono- and Multi-Objective Method for the Optimization of General UPS Parallel Manipulators

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 543
Author(s):  
Alejandra Ríos ◽  
Eusebio E. Hernández ◽  
S. Ivvan Valdez
Keyword(s):  
Genetic Algorithm ◽  
Performance Metrics ◽  
Tracking Error ◽  
Parallel Manipulators ◽  
Optimization Method ◽  
Statistical Hypothesis ◽  
Two Stage ◽  
Multi Objective ◽  
Second Stage ◽  
Conflicting Objectives

This paper introduces a two-stage method based on bio-inspired algorithms for the design optimization of a class of general Stewart platforms. The first stage performs a mono-objective optimization in order to reach, with sufficient dexterity, a regular target workspace while minimizing the elements’ lengths. For this optimization problem, we compare three bio-inspired algorithms: the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO), and the Boltzman Univariate Marginal Distribution Algorithm (BUMDA). The second stage looks for the most suitable gains of a Proportional Integral Derivative (PID) control via the minimization of two conflicting objectives: one based on energy consumption and the tracking error of a target trajectory. To this effect, we compare two multi-objective algorithms: the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic Algorithm-III (NSGA-III). The main contributions lie in the optimization model, the proposal of a two-stage optimization method, and the findings of the performance of different bio-inspired algorithms for each stage. Furthermore, we show optimized designs delivered by the proposed method and provide directions for the best-performing algorithms through performance metrics and statistical hypothesis tests.

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