Computing the Moments of Polling Models with Batch Poisson Arrivals by Transform Inversion

2019 ◽  
Vol 31 (3) ◽  
pp. 515-526
Author(s):  
Wu-Lin Chen
Keyword(s):  
Polling Models ◽  
Poisson Arrivals

scholarly journals Polling Systems and Their Application to Telecommunication Networks

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 117
Author(s):  
Vladimir Vishnevsky ◽  
Olga Semenova
Keyword(s):  
System Analysis ◽  
Telecommunication Networks ◽  
Performance Characteristics ◽  
Transport Systems ◽  
Management Systems ◽  
Polling Systems ◽  
Polling System ◽  
Value Analysis ◽  
Polling Models ◽  
Poisson Arrivals

The paper presents a review of papers on stochastic polling systems published in 2007–2020. Due to the applicability of stochastic polling models, the researchers face new and more complicated polling models. Stochastic polling models are effectively used for performance evaluation, design and optimization of telecommunication systems and networks, transport systems and road management systems, traffic, production systems and inventory management systems. In the review, we separately discuss the results for two-queue systems as a special case of polling systems. Then we discuss new and already known methods for polling system analysis including the mean value analysis and its application to systems with heavy load to approximate the performance characteristics. We also present the results concerning the specifics in polling models: a polling order, service disciplines, methods to queue or to group arriving customers, and a feedback in polling systems. The new direction in the polling system models is an investigation of how the customer service order within a queue affects the performance characteristics. The results on polling systems with correlated arrivals (MAP, BMAP, and the group Poisson arrivals simultaneously to all queues) are also considered. We briefly discuss the results on multi-server, non-discrete polling systems and application of polling models in various fields.

scholarly journals IMPROVING THE PERFORMANCE OF POLLING MODELS USING FORCED IDLE TIMES

2017 ◽  
Vol 32 (4) ◽  
pp. 580-602
Author(s):  
Frank Aurzada ◽  
Sebastian Schwinn
Keyword(s):  
Polling Models ◽  
Queueing Delay ◽  
Wait And See ◽  
Poisson Arrivals ◽  
The Mean ◽  
Waiting Periods ◽  
General Service

We consider polling models in the sense of Takagi [19]. In our case, the feature of the server is that it may be forced to wait idly for new messages at an empty queue instead of switching to the next station. We propose four different wait-and-see strategies that govern these waiting periods. We assume Poisson arrivals for new messages and allow general service and switchover time distributions. The results are formulas for the mean average queueing delay and characterizations of the cases where the wait-and-see strategies yield a lower delay compared with the exhaustive strategy.

Tollbooth tandem queues with infinite homogeneous servers

2015 ◽  
Vol 52 (4) ◽  
pp. 941-961 ◽  
Author(s):  
Xiuli Chao ◽  
Qi-Ming He ◽  
Sheldon Ross
Keyword(s):  
Performance Measures ◽  
System Performance ◽  
Stochastic Ordering ◽  
Tandem Queues ◽  
Poisson Arrival ◽  
Arrival Processes ◽  
Poisson Arrivals ◽  
Number Of Customers ◽  
Steady State Solutions ◽  
Transient And Steady State

In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Both transient and steady state solutions are derived first for Poisson arrivals, and then extended to cases with batch Poisson and nonstationary Poisson arrival processes. Finally, we report several stochastic ordering results on how system performance measures are affected by arrival and service processes.

scholarly journals Performance Evaluation of Cloud Data Centers with Batch Task Arrivals

2013 ◽  
pp. 199-223 ◽  
Author(s):  
Hamzeh Khazaei ◽  
Jelena Mišić ◽  
Vojislav B. Mišić
Keyword(s):  
Performance Evaluation ◽  
Queue Length ◽  
Blocking Probability ◽  
General Distribution ◽  
Cloud Data ◽  
Wide Range ◽  
Accurate Performance ◽  
Cloud Data Centers ◽  
Poisson Arrivals

Accurate performance evaluation of cloud computing resources is a necessary prerequisite for ensuring that Quality of Service (QoS) parameters remain within agreed limits. In this chapter, the authors consider cloud centers with Poisson arrivals of batch task requests under total rejection policy; task service times are assumed to follow a general distribution. They describe a new approximate analytical model for performance evaluation of such systems and show that important performance indicators such as mean request response time, waiting time in the queue, queue length, blocking probability, probability of immediate service, and probability distribution of the number of tasks in the system can be obtained in a wide range of input parameters.

Numerical solution to limited service polling models

1986 ◽  
Vol 9 (4) ◽  
pp. 171-176 ◽  
Author(s):  
JF Hayes ◽  
A Jalali-Nadushan
Keyword(s):  
Numerical Solution ◽  
Polling Models ◽  
Limited Service
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