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 (say class-1 and class-2). We assume that the scheduling discipline in our work is FCFS. We assume that if we have at least one class-2 customer 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 a class-2 customer. 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.
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References
De Clercq, S., Steyaert, B., Bruneel, H.: Queue content analysis in a 2-class discrete-time queueing system under the slot-bound priority service rule. Math. Prob. Eng. 2012 (2012)
De Clercq, S., Laevens, K., Steyaert, B., Bruneel, H.: A multi-class discrete-time queueing system under the FCFS service discipline. Ann. Oper. Res. 202(1), 59–73 (2013)
Baetens, J., Steyaert, B., Claeys, D., Bruneel, H.: Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times. Perform. Eval. 135, 102012 (2019)
Walraevens, J., Bruneel, H., Fiems, D., Wittevrongel, S.: Delay analysis of multiclass queues with correlated train arrivals and a hybrid priority/FIFO scheduling discipline. Appl. Math. Model. 45, 823–839 (2017)
Van Houdt, B., Blondia, C.: The delay distribution of a type k customer in a first-come-first-served MMAP [K]/PH[K]/1 queue. J. Appl. Probab. 39, 213–223 (2002)
De Clercq, S., Walraevens, J.: Delay analysis of a two-class priority queue with external arrivals and correlated arrivals from another node. Ann. Oper. Res. 293(1), 57–72 (2020)
Takine, T.: Single-server queues with Markov-modulated arrivals and service speed. Queueing Syst. 49(1), 7–22 (2005)
Wittevrongel, S., Feyaerts, B., Bruneel, H., De Vuyst, S.: Delay characteristics in place-reservation queues with class-dependent service times. J. Ind. Manage. Optim. 15(1), 37–58 (2019)
Boxma, O.J., Takine, T.: The M/G/1 FIFO queue with several customer classes. Queueing Syst. 45(3), 185 (2003)
Kim, B., Kim, J.: Stability of a multi-class multi-server retrial queueing system with service times depending on classes and servers. Queueing Syst. 94(1), 129–146 (2020)
Miller, R.G., Jr.: Priority queues. Ann. Math. Stat. 31(1), 86–103 (1960)
Maertens, T., Walraevens, J., Bruneel, H.: Priority queueing systems: from probability generating functions to tail probabilities. Queueing Syst. 55(1), 27–39 (2007)
Walraevens, J., Steyaert, B., Bruneel, H.: A preemptive repeat priority queue with resampling: performance analysis. Ann. Oper. Res. 146(1), 189–202 (2006)
Fiems, D., Walraevens, J., Bruneel, H.: Performance of a partially shared priority buffer with correlated arrivals. In: Mason, L., Drwiega, T., Yan, J. (eds.) ITC 2007. LNCS, vol. 4516, pp. 582–593. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72990-7_52
Maertens, T., Walraevens, J., Bruneel, H.: On priority queues with priority jumps. Perform. Eval. 63(12), 1235–1252 (2006)
De Muynck, M., Bruneel, H., Wittevrongel, S.: Analysis of a queue with general service demands and correlated service capacities. Ann. Oper. Res. 293(1), 73–99 (2020)
Bruneel, H., Kim, B.G.: Discrete-time models for communication systems including ATM. Kluwer Academic Publishers, Boston (1993)
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This work was supported in part by an EOS grant from the Belgian Research Councils FWO and FNRS (grant number 30452698) and in part by a research project from the Flemish Research Council FWO (grant number 3G051118).
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Sasaninejad, S., Walraevens, J., Moradi, H., Wittevrongel, S. (2023). System Content Analysis for a Two-Class Queue Where Service Times in a Busy Period Depend on the Presence of Class-2. In: Hyytiä, E., Kavitha, V. (eds) Performance Evaluation Methodologies and Tools. VALUETOOLS 2022. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 482. Springer, Cham. https://doi.org/10.1007/978-3-031-31234-2_4
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DOI: https://doi.org/10.1007/978-3-031-31234-2_4
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