Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

2021 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Ayyappan G ◽  
Nirmala Marimuthu
Keyword(s):  
Queueing System ◽  
Arrival Rate ◽  
Multiple Vacation

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.

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