# American Institute of Mathematical Sciences

• Previous Article
The inexact log-exponential regularization method for mathematical programs with vertical complementarity constraints
• JIMO Home
• This Issue
• Next Article
Multiserver retrial queue with setup time and its application to data centers
January  2019, 15(1): 37-58. doi: 10.3934/jimo.2018031

## Delay characteristics in place-reservation queues with class-dependent service times

 1 SMACS Research Group, Department TELIN, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium 2 Department of Industrial Systems Engineering and Product Design, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium

* Corresponding author: Sabine Wittevrongel

The reviewing process of this paper was handled by Yutaka Takahashi and Wuyi Yue

Received  March 2017 Revised  July 2017 Published  February 2018

This paper considers a discrete-time single-server infinite-capacity queue with two classes of packet arrivals, either delay-sensitive (class 1) or delay-tolerant (class 2), and a reservation-based priority scheduling mechanism. The objective is to provide a better quality of service to delay-sensitive packets at the cost of allowing higher delays for the best-effort packets. To this end, the scheduling mechanism makes use of an in-queue reserved place intended for future class-1 packet arrivals. A class-1 arrival takes the place of the reservation in the queue, after which a new reservation is created at the tail of the queue. Class-2 arrivals always take place at the tail of the queue. We study the delay characteristics for both packet classes under the assumption of a general independent packet arrival process. The service times of the packets are independent and have a general distribution that depends on the class of the packet. Closed-form expressions are obtained for the probability generating functions of the per-class delays. From this, moments and tail probabilities of the packet delays of both classes are derived. The results are illustrated by some numerical examples.

Citation: Sabine Wittevrongel, Bart Feyaerts, Herwig Bruneel, Stijn De Vuyst. Delay characteristics in place-reservation queues with class-dependent service times. Journal of Industrial & Management Optimization, 2019, 15 (1) : 37-58. doi: 10.3934/jimo.2018031
##### References:

show all references

##### References:
Insertion of 4 packets arriving during the same slot under reservation-based scheduling
Sample path of the queueing model
An $M\times M$ switch with output buffers
Mean packet delays versus load $\rho$, for $M = 16$, $\mu_1 = \mu_2 = 3$ and various values of $\alpha$
Mean packet delays versus load $\rho$, for $M = 16$, $\mu_1 = 3$, $\mu_2 = 20$ and various values of $\alpha$
Standard deviations of packet delays versus load $\rho$, for $M = 16$, $\mu_1 = 3$, $\mu_2 = 20$ and various values of $\alpha$
Tail probabilities of the packet delays, for $M = 16$, $\rho = 0.8$, $\mu_1 = 3$, $\mu_2 = 20$ and various values of $\alpha$
Tail probabilities of the packet delays, for $M = 16$, $\rho = 0.8$, $\alpha = 0.15$, $\mu_2 = 4$ and various values of $\mu_1$
Tail probabilities of the packet delays, for $M = 16$, $\rho = 0.8$, $\alpha = 0.15$, $\mu_2 = 4$ and various values of $\mu_2$
Mean packet delays versus the standard deviation of the class-1 service times $\sigma_1$, for $M = 16$, $\rho = 0.8$, $\mu_1 = \mu_2 = 3$ and various values of $\alpha$
Mean packet delays versus the standard deviation of the class-2 service times $\sigma_2$, for $M = 16$, $\rho = 0.8$, $\mu_1 = \mu_2 = 3$ and various values of $\alpha$
Mean values and standard deviations of packet delays versus traffic mix $\alpha$, for $M = 16$, $\rho = 0.8$, and $\mu_1 = \mu_2 = 3$
 [1] Yung Chung Wang, Jenn Shing Wang, Fu Hsiang Tsai. Analysis of discrete-time space priority queue with fuzzy threshold. Journal of Industrial & Management Optimization, 2009, 5 (3) : 467-479. doi: 10.3934/jimo.2009.5.467 [2] Bart Feyaerts, Stijn De Vuyst, Herwig Bruneel, Sabine Wittevrongel. The impact of the $NT$-policy on the behaviour of a discrete-time queue with general service times. Journal of Industrial & Management Optimization, 2014, 10 (1) : 131-149. doi: 10.3934/jimo.2014.10.131 [3] Michiel De Muynck, Herwig Bruneel, Sabine Wittevrongel. Analysis of a discrete-time queue with general service demands and phase-type service capacities. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1901-1926. doi: 10.3934/jimo.2017024 [4] Sofian De Clercq, Koen De Turck, Bart Steyaert, Herwig Bruneel. Frame-bound priority scheduling in discrete-time queueing systems. Journal of Industrial & Management Optimization, 2011, 7 (3) : 767-788. doi: 10.3934/jimo.2011.7.767 [5] Shaojun Lan, Yinghui Tang. Performance analysis of a discrete-time $Geo/G/1$ retrial queue with non-preemptive priority, working vacations and vacation interruption. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1421-1446. doi: 10.3934/jimo.2018102 [6] Gopinath Panda, Veena Goswami. Effect of information on the strategic behavior of customers in a discrete-time bulk service queue. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1369-1388. doi: 10.3934/jimo.2019007 [7] Gábor Horváth, Zsolt Saffer, Miklós Telek. Queue length analysis of a Markov-modulated vacation queue with dependent arrival and service processes and exhaustive service policy. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1365-1381. doi: 10.3934/jimo.2016077 [8] Chuandong Li, Fali Ma, Tingwen Huang. 2-D analysis based iterative learning control for linear discrete-time systems with time delay. Journal of Industrial & Management Optimization, 2011, 7 (1) : 175-181. doi: 10.3934/jimo.2011.7.175 [9] Bara Kim, Jeongsim Kim. Explicit solution for the stationary distribution of a discrete-time finite buffer queue. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1121-1133. doi: 10.3934/jimo.2016.12.1121 [10] Zhanyou Ma, Wenbo Wang, Linmin Hu. Performance evaluation and analysis of a discrete queue system with multiple working vacations and non-preemptive priority. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1135-1148. doi: 10.3934/jimo.2018196 [11] Hideaki Takagi. Unified and refined analysis of the response time and waiting time in the M/M/m FCFS preemptive-resume priority queue. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1945-1973. doi: 10.3934/jimo.2017026 [12] A. Azhagappan, T. Deepa. Transient analysis of N-policy queue with system disaster repair preventive maintenance re-service balking closedown and setup times. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-14. doi: 10.3934/jimo.2019083 [13] Arnaud Devos, Joris Walraevens, Tuan Phung-Duc, Herwig Bruneel. Analysis of the queue lengths in a priority retrial queue with constant retrial policy. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-30. doi: 10.3934/jimo.2019082 [14] Xiang Xie, Honglei Xu, Xinming Cheng, Yilun Yu. Improved results on exponential stability of discrete-time switched delay systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 199-208. doi: 10.3934/dcdsb.2017010 [15] Jianquan Li, Zhien Ma, Fred Brauer. Global analysis of discrete-time SI and SIS epidemic models. Mathematical Biosciences & Engineering, 2007, 4 (4) : 699-710. doi: 10.3934/mbe.2007.4.699 [16] Ping Yan, Ji-Bo Wang, Li-Qiang Zhao. Single-machine bi-criterion scheduling with release times and exponentially time-dependent learning effects. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1117-1131. doi: 10.3934/jimo.2018088 [17] Shan Gao, Jinting Wang. On a discrete-time GI$^X$/Geo/1/N-G queue with randomized working vacations and at most $J$ vacations. Journal of Industrial & Management Optimization, 2015, 11 (3) : 779-806. doi: 10.3934/jimo.2015.11.779 [18] Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial & Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167 [19] Pikkala Vijaya Laxmi, Singuluri Indira, Kanithi Jyothsna. Ant colony optimization for optimum service times in a Bernoulli schedule vacation interruption queue with balking and reneging. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1199-1214. doi: 10.3934/jimo.2016.12.1199 [20] Pikkala Vijaya Laxmi, Obsie Mussa Yesuf. Analysis of a finite buffer general input queue with Markovian service process and accessible and non-accessible batch service. Journal of Industrial & Management Optimization, 2010, 6 (4) : 929-944. doi: 10.3934/jimo.2010.6.929

2018 Impact Factor: 1.025