Research Article
System Content Analysis for a Two-Class Queue Where Service Times in a Busy Period Depend on the Presence of Class-2
@INPROCEEDINGS{10.1007/978-3-031-31234-2_4, author={Sara Sasaninejad and Joris Walraevens and Hossein Moradi and Sabine Wittevrongel}, title={System Content Analysis for a Two-Class Queue Where Service Times in a Busy Period Depend on the Presence of Class-2}, proceedings={Performance Evaluation Methodologies and Tools. 15th EAI International Conference, VALUETOOLS 2022, Virtual Event, November 2022, Proceedings}, proceedings_a={VALUETOOLS}, year={2023}, month={5}, keywords={Multi-class queueing systems Dependent service times System content}, doi={10.1007/978-3-031-31234-2_4} }- Sara Sasaninejad
Joris Walraevens
Hossein Moradi
Sabine Wittevrongel
Year: 2023
System Content Analysis for a Two-Class Queue Where Service Times in a Busy Period Depend on the Presence of Class-2
VALUETOOLS
Springer
DOI: 10.1007/978-3-031-31234-2_4
Abstract
Since many real-world queueing systems are meant to incorporate heterogeneous customers, the analysis of multi-class queueing models has been an area of active research. A review of the associated models shows, however, that multi-class queueing systems in which service times depend on the presence of one certain class of customers have not yet been extensively analyzed. To address this research gap, we consider an infinite-capacity single-server discrete-time queueing system with two classes of customers (sayclass-1andclass-2). We assume that the scheduling discipline in our work is FCFS. We assume that if we have at least oneclass-2customer during an ongoing busy period (until the system becomes empty), the service time distributions of all the customers change to the service time distribution of aclass-2customer. By further considering the number of customer arrivals of each class to be independent and identically distributed (with a general probability distribution) from slot to slot, we perform the system content analysis by means of a generating function based approach. The results of this analysis reveal that the incorporation of such an interdependency in the service process significantly affects the resulting system content, as compared to a model where the service times are completely attached to the customer classes.
