scholarly journals Truncated Erlangian Queueing System with Fuzzy Arrival Rate, Balking and Reneging

2011 ◽  
Vol 3 (4) ◽  
pp. 379-384
Author(s):  
A. Pourdarvish ◽  
M. Shokry
Keyword(s):  
Queueing System ◽  
Arrival Rate

THE ALLOCATION OF CUSTOMERS IN A DISCRETE-TIME MULTI-SERVER QUEUEING SYSTEM

2010 ◽  
Vol 27 (06) ◽  
pp. 649-667 ◽  
Author(s):  
WEI SUN ◽  
NAISHUO TIAN ◽  
SHIYONG LI
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Queueing System ◽  
Arrival Rate ◽  
Allocation Problem ◽  
Optimal Outcome ◽  
The Subject ◽  
Multi Server ◽  
Theoretical Results

This paper, analyzes the allocation problem of customers in a discrete-time multi-server queueing system and considers two criteria for routing customers' selections: equilibrium and social optimization. As far as we know, there is no literature concerning the discrete-time multi-server models on the subject of equilibrium behaviors of customers and servers. Comparing the results of customers' distribution at the servers under the two criteria, we show that the servers used in equilibrium are no more than those used in the socially optimal outcome, that is, the individual's decision deviates from the socially preferred one. Furthermore, we also clearly show the mutative trend of several important performance measures for various values of arrival rate numerically to verify the theoretical results.

scholarly journals Equilibrium and Optimization in a Double-Ended Queueing System with Dynamic Control

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Yuejiao Wang ◽  
Zaiming Liu
Keyword(s):  
Queueing System ◽  
Service System ◽  
Dynamic Control ◽  
Optimal Strategies ◽  
Control Policy ◽  
Arrival Rate ◽  
Social Benefit ◽  
Equilibrium Strategies ◽  
Taxi Service ◽  
The Relationship

In this paper, we consider a double-ended queueing system which is a passenger-taxi service system. In our model, we also consider the dynamic taxi control policy which means that the manager adjusts the arrival rate of taxis according to the taxi stand congestion. Under three different information levels, we study the equilibrium strategies as well as socially optimal strategies for arriving passengers by a reward-cost structure. Furthermore, we present several numerical experiments to analyze the relationship between the equilibrium and socially optimal strategies and demonstrate the effect of different information levels as well as several parameters on social benefit.

Adaptation of the service capacity in a queueing system which is subjected to a change in the arrival rate at unknown epoch

1978 ◽  
Vol 10 (3) ◽  
pp. 666-681 ◽  
Author(s):  
M. Yadin ◽  
S. Zacks
Keyword(s):  
Exponential Distribution ◽  
Queueing System ◽  
Arrival Rate ◽  
Cost Structure ◽  
Service Capacity ◽  
Service Intensity ◽  
Discounted Cost ◽  
Adaptation Policies ◽  
The Cost ◽  
Optimal Adaptation

The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arrival rate λ0 of customers shifts at unknown epoch, τ, to a known value, λ1. The service intensity of the system starts at μ0 and can be increased at most N times to μ1 < μ2 < · · · < μN. The cost structure consists of the cost changing μi to μj (i + 1 ≦ j ≦ N); of maintaining service at rate μ (per unit of time) and of holding customers at the station (per unit of time). Adaptation policies are constrained by the fact that μ can be only increased. A Bayes solution is derived, under the prior assumption that τ has an exponential distribution. This solution minimizes the total expected discounted cost for the entire future.

A note on the convexity of performance measures of M/M/c queueing systems

1983 ◽  
Vol 20 (04) ◽  
pp. 920-923 ◽  
Author(s):  
Hau Leung Lee ◽  
Morris A. Cohen
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Control Problems ◽  
Traffic Intensity ◽  
Expected Number ◽  
Expected Waiting Time

Convexity of performance measures of queueing systems is important in solving control problems of multi-facility systems. This note proves that performance measures such as the expected waiting time, expected number in queue, and the Erlang delay formula are convex with respect to the arrival rate or the traffic intensity of the M/M/c queueing system.

scholarly journals Improving Queuing System with Limited Resources using TRIZ and Arena Simulation

2020 ◽  
Vol 9 (7) ◽  
pp. 911-919
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Research Work ◽  
Arrival Rate ◽  
Time Dependent ◽  
Limited Resources ◽  
Time Interval ◽  
Stationary Time

A university cafeteria is a queueing system characterised by non-stationary time of arrival with limited resources where the arrival rate is time dependent and has different pattern of arrival for different time interval. This means at certain time of the day; the arrival rate is much higher than other time. For a university cafeteria, the arrival rate of customer during the lunchtime is higher and the food (resources) is limited. Non-stationary time dependent queueing systems are not easily modelled mathematically hence such queueing systems are modelled using simulation tools such as ARENA. In order to model a non-stationary time dependent queueing system with limited resources and solve queueing problems using ARENA, researchers have to rely on their knowledge and experience to identify the appropriate parameters of the system and make modifications to these parameters of the system to solve queueing problems by means of trial and error. Hence, this research work explores the potentials of applying a systematic problem solving tool, TRIZ to help users to make better decisions in deriving solutions to improve a non-stationary time dependent queueing system with limited resources. A case study was carried out to minimize the waiting time of the customers at the cafeteria of the Faculty of Engineering, Universiti Putra Malaysia (UPM), which has queueing problems for years during lunchtime. TRIZ was applied in this case study and the results showed that TRIZ can assist researchers to derive a solution model that leads to shorter waiting time without incurring additional cost and resources.

scholarly journals On the virtual waiting time for an M/G/1 retrial queue with two types of calls

1993 ◽  
Vol 6 (1) ◽  
pp. 11-23 ◽  
Author(s):  
Bong Dae Choi ◽  
Dong Hwan Han ◽  
Guennadi Falin
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Retrial Queue ◽  
Arrival Rate ◽  
Switching System ◽  
Stieltjes Transform ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Virtual Waiting Time ◽  
Incoming Call

We consider an M/G/1 retrial queueing system with two types of calls which models a telephone switching system. In the case that arriving calls are blocked due to the channel being busy, the outgoing calls are queued in priority group whereas the incoming calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the Laplace-Stieltjes transform of the distribution of the virtual waiting time for an incoming call. When the arrival rate of outgoing calls is zero, it is shown that our result is consistent with the known result for a retrial queueing system with one type of call.

Sign in / Sign up

Export Citation Format

Share Document