scholarly journals Controlling arrival and service rates to reduce sensitivity of queueing systems with customer abandonment

2021 ◽  
pp. 100089
Author(s):  
Katsunobu Sasanuma ◽  
Robert Hampshire ◽  
Alan Scheller-Wolf
Keyword(s):  
Queueing Systems ◽  
Customer Abandonment ◽  
Service Rates

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 Stability of Parallel Queueing Systems with Coupled Service Rates

2007 ◽  
Vol 18 (4) ◽  
pp. 447-472 ◽  
Author(s):  
Sem Borst ◽  
Matthieu Jonckheere ◽  
Lasse Leskelä
Keyword(s):  
Queueing Systems ◽  
Service Rates

scholarly journals Markovian Queueing System with Discouraged Arrivals and Self-Regulatory Servers

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
K. V. Abdul Rasheed ◽  
M. Manoharan
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Multiple Servers ◽  
Special Cases ◽  
Service Rates ◽  
Expected Waiting Time ◽  
Number Of Customers ◽  
Steady State Probabilities

We consider discouraged arrival of Markovian queueing systems whose service speed is regulated according to the number of customers in the system. We will reduce the congestion in two ways. First we attempt to reduce the congestion by discouraging the arrivals of customers from joining the queue. Secondly we reduce the congestion by introducing the concept of service switches. First we consider a model in which multiple servers have three service ratesμ1,μ2, andμ(μ1≤μ2<μ), say, slow, medium, and fast rates, respectively. If the number of customers in the system exceeds a particular pointK1orK2, the server switches to the medium or fast rate, respectively. For this adaptive queueing system the steady state probabilities are derived and some performance measures such as expected number in the system/queue and expected waiting time in the system/queue are obtained. Multiple server discouraged arrival model having one service switch and single server discouraged arrival model having one and two service switches are obtained as special cases. A Matlab program of the model is presented and numerical illustrations are given.

Subdiffusive Load Balancing in Time-Varying Queueing Systems

2019 ◽  
Vol 67 (6) ◽  
pp. 1678-1698
Author(s):  
Rami Atar ◽  
Isaac Keslassy ◽  
Gal Mendelson
Keyword(s):  
Load Balancing ◽  
Queue Length ◽  
Queueing Systems ◽  
Load Condition ◽  
Service Rates ◽  
Queue Lengths ◽  
Join The Shortest Queue ◽  
The Difference ◽  
Shortest Queue ◽  
Diffusion Scale

The degree to which delays or queue lengths equalize under load-balancing algorithms gives a good indication of their performance. Some of the most well-known results in this context are concerned with the asymptotic behavior of the delay or queue length at the diffusion scale under a critical load condition, where arrival and service rates do not vary with time. For example, under the join-the-shortest-queue policy, the queue length deviation process, defined as the difference between the greatest and smallest queue length as it varies over time, is at a smaller scale (subdiffusive) than that of queue lengths (diffusive).

Generalised birth and death queueing processes: recent results

1977 ◽  
Vol 9 (1) ◽  
pp. 125-140 ◽  
Author(s):  
B. W. Conolly ◽  
J. Chan
Keyword(s):  
Waiting Time ◽  
Queueing Systems ◽  
System Size ◽  
Single Server ◽  
Traffic Intensity ◽  
Stable Regime ◽  
Mean Waiting Time ◽  
Service Rates ◽  
Queueing Processes ◽  
Effective Service

The systems considered are single-server, though the theory has wider application to models of adaptive queueing systems. Arrival and service mechanisms are governed by state (n)-dependent mean arrival and service rates λn and µn. It is assumed that the choice of λn and µn leads to a stable regime. Formulae are sought that provide easy means of computing statistics of effectiveness of systems. A measure of traffic intensity is first defined in terms of ‘effective’ service time and inter-arrival intervals. It is shown that the latter have a renewal type connection with appropriately defined mean effective arrival and service rates λ∗ and µ∗ and that in consequence the ratio λ∗/µ∗ is the traffic intensity, equal moreover to where is the stable probability of an empty system, consistent with other systems. It is also shown that for first come, first served discipline the equivalent of Little's formula holds, where and are the mean waiting time of an arrival and mean system size at an arbitrary epoch. In addition it appears that stable regime output intervals are statistically identical with effective inter-arrival intervals. Symmetrical moment formulae of arbitrary order are derived algebraically for effective inter-arrival and service intervals, for waiting time, for busy period and for output.

A NOTE ON INFINITE-SERVER MARKOV MODULATED AND SINGLE-SERVER RETRIAL QUEUES

2014 ◽  
Vol 31 (02) ◽  
pp. 1440003
Author(s):  
ZHE DUAN ◽  
MELIKE BAYKAL-GÜRSOY
Keyword(s):  
Queueing Systems ◽  
Retrial Queue ◽  
System Size ◽  
Retrial Queues ◽  
Stochastic Decomposition ◽  
Applied Probability ◽  
Single Server ◽  
The Matrix ◽  
Service Rates ◽  
Markov Modulated

We reconsider the M/M/∞ queue with two-state Markov modulated arrival and service processes and the single-server retrial queue analyzed in Keilson and Servi [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471]. Fuhrmann and Cooper type stochastic decomposition holds for the stationary occupancy distributions in both queues [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471; Baykal-Gürsoy, M and W Xiao (2004). Stochastic decomposition in M/M/∞ queues with Markov-modulated service rates. Queueing Systems, 48, 75–88]. The main contribution of the present paper is the derivation of the explicit form of the stationary system size distributions. Numerical examples are presented visually exhibiting the effect of various parameters on the stationary distributions.

DYNAMIC CONTROL OF A SINGLE-SERVER SYSTEM WHEN JOBS CHANGE STATUS

2017 ◽  
Vol 32 (3) ◽  
pp. 353-395
Author(s):  
Gabriel Zayas-Cabán ◽  
Hyun-Soo Ahn
Keyword(s):  
Queueing Systems ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Single Server ◽  
Priority Rules ◽  
Holding Costs ◽  
Class 1 ◽  
Markov Decision ◽  
Service Rates ◽  
Customer Model

From health care to maintenance shops, many systems must contend with allocating resources to customers or jobs whose initial service requirements or costs change when they wait too long. We present a new queueing model for this scenario and use a Markov decision process formulation to analyze assignment policies that minimize holding costs. We show that the classic cμ rule is generally not optimal when service or cost requirements can change. Even for a two-class customer model where a class 1 task becomes a class 2 task upon waiting, we show that additional orderings of the service rates are needed to ensure the optimality of simple priority rules. We then show that seemingly-intuitive switching curve structures are also not optimal in general. We study these scenarios and provide conditions under which they do hold. Lastly, we show that results from the two-class model do not extend to when there are n≥3 customer classes. More broadly, we find that simple priority rules are not optimal. We provide sufficient conditions under which a simple priority rule holds. In short, allowing service and/or cost requirements to change fundamentally changes the structure of the optimal policy for resource allocation in queueing systems.

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