On effects of arrival rate and burstiness in the queueing system: Analysis ofLb/D/1

1996 ◽  
Vol 22 (1-2) ◽  
pp. 175-188 ◽  
Author(s):  
Daniel Chonghwan Lee
Keyword(s):  
System Analysis ◽  
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.

FORECAST ERRORS IN SERVICE SYSTEMS

2009 ◽  
Vol 23 (2) ◽  
pp. 305-332 ◽  
Author(s):  
Samuel G. Steckley ◽  
Shane G. Henderson ◽  
Vijay Mehrotra
Keyword(s):  
System Analysis ◽  
Service System ◽  
Arrival Rate ◽  
Forecast Errors ◽  
Normal Mixture ◽  
Large Dataset ◽  
Long Run ◽  
Great Generality ◽  
Short Run ◽  
Timely Fashion

We investigate the presence and impact of forecast errors in the arrival rate of customers to a service system. Analysis of a large dataset shows that forecast errors can be large relative to the fluctuations naturally expected in a Poisson process. We show that ignoring forecast errors typically leads to overestimates of performance and that forecast errors of the magnitude seen in our dataset can have a practically significant impact on predictions of long-run performance. We also define short-run performance as the random percentage of calls received in a particular period that are answered in a timely fashion. We prove a central limit theorem that yields a normal-mixture approximation for its distribution for Markovian queues and we sketch an argument that shows that a normal-mixture approximation should be valid in great generality. Our results provide motivation for studying staffing strategies that are more flexible than the fixed-level staffing rules traditionally studied in the literature.

scholarly journals Lower bound for average delay in unblocked random access algorithm with orthogonal preambles

2020 ◽  
pp. 79-85
Author(s):  
Artem Burkov ◽  
Seva Shneer ◽  
Andrey Turlikov
Keyword(s):  
Lower Bound ◽  
Resource Sharing ◽  
Queuing Theory ◽  
Multiple Access ◽  
System Analysis ◽  
Random Access ◽  
Arrival Rate ◽  
High Energy ◽  
Average Delay ◽  
Closed Expression

Introduction: Currently, the first versions of 5G communication standard networks are being deployed and discussions are underway on the further development of cellular networks and the transition to the 6G standard. The work of the currently popular idea of ​​the Internet of Things (IoT) is supposed to be in the framework of a Massive Machine-Type Communications scenario, which has a number of requirements for operation characteristics: very high energy efficiency, relatively low delay and fairly reliable communication. It is assumed that random multiple access procedures are used, since, due to the nature of the traffic, it is impossible to develop a channel resource sharing policy. To increase the efficiency of random access, a class of unblocked algorithms using orthogonal preambles can be used. Purpose: to calculate the lower bound of the average delay for the class of unblocked random multiple access algorithms using orthogonal preambles. Methods: system analysis, a theory of random processes, queuing theory, and simulation. Results: A model of a system with a potentially unlimited number of users who use random unblocked access to transmit data over a common communication channel using orthogonal preambles is proposed. A closed expression is obtained for calculating the lower bound of the average delay in such a system depending on the intensity of the input arrival rate. The limit value of the intensity of the input arrival rate to which the system operates stably is determined. Shown are the results of simulation with respect to the obtained bound. Practical relevance: the obtained boundary allows us to estimate the lower average delay in the described class of algorithms. Its application allows us to determine the possibility of using the considered class of algorithms from the point of view of limitations on the average delay at the stage of designing random multiple access systems.

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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