Analysis of tandem polling queues with finite buffers
- PDF / 830,375 Bytes
- 27 Pages / 439.37 x 666.142 pts Page_size
- 86 Downloads / 229 Views
Analysis of tandem polling queues with finite buffers Ravi Suman1
· Ananth Krishnamurthy2
© Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract We analyze a tandem polling queue with two stations operating under three different polling strategies, namely: (1) Independent polling, (2) Synchronous polling, and (3) Out-of-sync polling. Under Markovian assumptions of arrival and service times, we conduct an exact analysis using Matrix Geometric method to determine system throughput, mean queue lengths, and mean waiting times. Through numerical experiments, we compare the performance of the three polling strategies and the effect of buffer sizes on performance. We observe that the independent polling strategy generally performs better than the other strategies, however, under certain settings of product asymmetry, other strategies yield better performance. Keywords Polling queues · Finite buffers · Performance analysis
1 Introduction A polling queue consists of a single server station serving customers from different queues in a fixed order. Polling queues are often used to model systems where multiple types of customers compete for a common resource (server). In manufacturing, polling queues have been used to model flow of multiple products undergoing manufacturing operations in a factory (Federgruen and Katalan 1996). In healthcare, polling queues have been used to model the flow of different types of patients through various activities in a hospital or clinic (Boon and Adan 2009). In transportation, polling queues have been used to model multiple traffic flows in a transportation network (Boon et al. 2010; Takagi 2000). The design of a polling queue involves several decisions related to service discipline, queueing discipline, and buffer capacity. Polling queues are generally classified into four types based on service discipline, namely, exhaustive, gated, customer-limited, and time-limited polling queues. The service discipline dictates how long the server processes customers of one type from
B
Ravi Suman [email protected] Ananth Krishnamurthy [email protected]
1
Department of Industrial and Systems Engineering, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA
2
Decision Sciences, Indian Institute of Management Bangalore, Bannerghatta Road, Bangalore 560076, India
123
Annals of Operations Research
one of the queues before switching to another queue to serve customers of a different type. The queueing discipline, such as first-come-first-served, priority, or last-come-first-served determines in what order the server processes customers from a particular queue. Depending on the application, polling queues can have infinite buffers or finite buffers which could lead to blocking and/or lost customers of a particular type. Takagi (2000) and Vishnevskii and Semenova (2006) provide a comprehensive survey of literature on the analysis of polling queues. While a majority of existing research on polling queues focus on the single-station polling queue, this
Data Loading...
