Rare events in series of queues

1992 ◽  
Vol 29 (1) ◽  
pp. 168-175 ◽  
Author(s):  
Pantelis Tsoucas
Keyword(s):  
Queueing Networks ◽  
Total Population ◽  
Large Deviation ◽  
Rare Event ◽  
Arrival Rate ◽  
Service Rate ◽  
Action Functional ◽  
In Series ◽  
Service Rates ◽  
Queues In Series

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

Rare events in series of queues

1992 ◽  
Vol 29 (01) ◽  
pp. 168-175 ◽  
Author(s):  
Pantelis Tsoucas
Keyword(s):  
Queueing Networks ◽  
Total Population ◽  
Large Deviation ◽  
Rare Event ◽  
Arrival Rate ◽  
Service Rate ◽  
Action Functional ◽  
In Series ◽  
Service Rates ◽  
Queues In Series

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

Optimal control of service rates in networks of queues

1987 ◽  
Vol 19 (1) ◽  
pp. 202-218 ◽  
Author(s):  
Richard R. Weber ◽  
Shaler Stidham
Keyword(s):  
Rate Control ◽  
Queueing Networks ◽  
Arrival Rate ◽  
Service Rate ◽  
Discounted Cost ◽  
Holding Costs ◽  
Optimal Service ◽  
Monotonicity Result ◽  
Service Rates ◽  
Number Of Customers

We prove a monotonicity result for the problem of optimal service rate control in certain queueing networks. Consider, as an illustrative example, a number of ·/M/1 queues which are arranged in a cycle with some number of customers moving around the cycle. A holding cost hi(xi) is charged for each unit of time that queue i contains xi customers, with hi being convex. As a function of the queue lengths the service rate at each queue i is to be chosen in the interval , where cost ci(μ) is charged for each unit of time that the service rate μis in effect at queue i. It is shown that the policy which minimizes the expected total discounted cost has a monotone structure: namely, that by moving one customer from queue i to the following queue, the optimal service rate in queue i is not increased and the optimal service rates elsewhere are not decreased. We prove a similar result for problems of optimal arrival rate and service rate control in general queueing networks. The results are extended to an average-cost measure, and an example is included to show that in general the assumption of convex holding costs may not be relaxed. A further example shows that the optimal policy may not be monotone unless the choice of possible service rates at each queue includes 0.

Optimal control of service rates in networks of queues

1987 ◽  
Vol 19 (01) ◽  
pp. 202-218 ◽  
Author(s):  
Richard R. Weber ◽  
Shaler Stidham
Keyword(s):  
Rate Control ◽  
Queueing Networks ◽  
Arrival Rate ◽  
Service Rate ◽  
Discounted Cost ◽  
Holding Costs ◽  
Optimal Service ◽  
Monotonicity Result ◽  
Service Rates ◽  
Number Of Customers

We prove a monotonicity result for the problem of optimal service rate control in certain queueing networks. Consider, as an illustrative example, a number of ·/M/1 queues which are arranged in a cycle with some number of customers moving around the cycle. A holding cost hi (xi ) is charged for each unit of time that queue i contains xi customers, with hi being convex. As a function of the queue lengths the service rate at each queue i is to be chosen in the interval , where cost ci (μ) is charged for each unit of time that the service rate μis in effect at queue i. It is shown that the policy which minimizes the expected total discounted cost has a monotone structure: namely, that by moving one customer from queue i to the following queue, the optimal service rate in queue i is not increased and the optimal service rates elsewhere are not decreased. We prove a similar result for problems of optimal arrival rate and service rate control in general queueing networks. The results are extended to an average-cost measure, and an example is included to show that in general the assumption of convex holding costs may not be relaxed. A further example shows that the optimal policy may not be monotone unless the choice of possible service rates at each queue includes 0.

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 Service Rate Optimization of Finite Population Queueing Model with State Dependent Arrival and Service Rates

2018 ◽  
Vol 13 (1) ◽  
pp. 60-68
Author(s):  
Sushil Ghimire ◽  
Gyan Bahadur Thapa ◽  
Ram Prasad Ghimire
Keyword(s):  
Finite Population ◽  
Arrival Rate ◽  
Service Rate ◽  
Queueing Model ◽  
State Dependent ◽  
Service Rates ◽  
Rate Optimization

 Providing service immediately after the arrival is rarely been used in practice. But there are some situations for which servers are more than the arrivals and no one has to wait to get served. In this model, arrival rate is

Optimization of Queuing Theory Based on Vague Environment

2016 ◽  
Vol 5 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Verónica Andrea González-López ◽  
Ramin Gholizadeh ◽  
Aliakbar M. Shirazi
Keyword(s):  
Everyday Life ◽  
Real World ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Service Rate ◽  
New Approach ◽  
The Real ◽  
Processing Times ◽  
Queuing Models ◽  
Service Rates

Waiting lines or queues are commonly occurred both in everyday life and in a variety of business and industrial situations. The various arrival rates, service rates and processing times of jobs/tasks usually assumed are exact. However, the real world is complex and the complexity is due to the uncertainty. The queuing theory by using vague environment is described in this paper. To illustrate, the approach analytical results for M/M/1/8 and M/M/s/8 systems are presented. It optimizes queuing models such that the arrival rate and service rate are vague numbers. This paper results a new approach for queuing models in the vague environment that it can be more effective than deterministic queuing models. A numerical example is illustrated to check the validity of the proposed method.

scholarly journals PENERAPAN METODE ANTRIAN DALAM MENENTUKAN FASILITAS YANG OPTIMAL PADA SPBU MAWADDAH

2018 ◽  
Vol 3 (5) ◽  
Author(s):  
Diana Khairani Sofyan ◽  
Sri Meutia
Keyword(s):  
Diesel Fuel ◽  
Arrival Rate ◽  
Service Level ◽  
Service Rate ◽  
Queuing Model ◽  
Fuel Pump ◽  
Gas Stations ◽  
Scenario Design ◽  
Service Rates ◽  
Number Of Customers

Gas stations Mawaddah Is one of the gas stations located in the Village Batuphat East Lhokseumawe. The gas station has 5 oil pumps consisting of premium with two pumps, diesel consists of two pumps, and pertamax consists of one pump. Preliminary data have been made regarding the arrival rate of vehicles in each pump, which is a two-wheeled premium filling pump of 195 vehicles, four or more 166 wheels or four wheels filling pumps, four or more diesel fuel pumps of 156 and a feeding pump of 138 vehicles. High vehicle arrival rate resulted in queue. To calculate the level of service has never been done so it is not known the maximum time for service on each pump. The research method used is queuing model related to arrival rate and service level, with result of research which obtained is vehicle arrival rate at each pump that is 2 wheel of premium gasoline pump is 2.59 minutes. The premium 4 wheels charging pump is 6.98. The 4 wheelers diesel fuel pump is 5.97 minutes and the first charging pump is 6.65 minutes with the facility number 1. Vehicle service rates of premium 2 and 4 wheelers are 15.52 minutes and 14.11 minutes, 4 wheel diesel fuel pump is 14.21 minutes and the first feed pump is 13.55 minutes with scenario design on each pump is Scenario 1 with 2 pumps, Probability of medium system empty 0.87500, Number of subscribers in the system and number of customers waiting in the queue of each 1 customer, the average customer time in the system 0.06696 minutes and waiting time as long as the customer in the queue 0.00030 minutes.Keywords: Queue, facility, arrival rate, service rate.

Realization factors and sensitivity analysis of queueing networks with state-dependent service rates

1990 ◽  
Vol 22 (1) ◽  
pp. 178-210 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Queueing Networks ◽  
Sample Path ◽  
Queueing Network ◽  
Service Rate ◽  
Steady State Probability ◽  
State Dependent ◽  
Service Rates ◽  
Realization Factors

The paper studies the sensitivity of the throughput with respect to a mean service rate in a closed queueing network with exponentially distributed service requirements and state-dependent service rates. The study is based on perturbation analysis of queueing networks. A new concept, the realization factor of a perturbation, is introduced. The properties of realization factors are discussed, and a set of equations specifying the realization factors are derived. The elasticity of the steady state throughput with respect to a mean service rate equals the product of the steady state probability and the corresponding realization factor. This elasticity can be estimated by applying a perturbation analysis algorithm to a sample path of the system. The sample path elasticity of the throughput with respect to a mean service rate converges with probability 1 to the elasticity of the steady state throughput. The theory provides an analytical method of calculating the throughput sensitivity and justifies the application of perturbation analysis.

scholarly journals Analysis of Fuzzy Non-preemptive Priority Queuing Model with Unequal Service Rate

2021 ◽  
Vol 12 (5) ◽  
pp. 1457-1460
Author(s):  
K. Selvakumari, Et. al.
Keyword(s):  
Performance Measures ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Arrival Rate ◽  
Triangular Fuzzy Number ◽  
Priority Queues ◽  
Service Rate ◽  
Preemptive Priority ◽  
Queuing Model ◽  
Service Rates

This article provides an effective method to analyze the performance measures of non-preemptive fuzzy priority queues with unequal service rates. Here the arrival rate and the service rate are in fuzzy numbers. Using a new ranking method, the fuzzy values are reduced to the crisp values. For that cause, both the Triangular Fuzzy Number (TFN) and Trapezoidal Fuzzy Number (TpFN) are chosen to establish the proposal's effectiveness. An illustration is given to find the efficiency of the performance measures of the fuzzy queuing model.

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