On a Multiserver Queueing System with Customers’ Impatience Until the End of Service Under Single and Multiple Vacation Policies

This paper deals with a multiserver queueing system with Bernoulli feedback and impatient customers (balking and reneging) under synchronous multiple and single vacation policies. Reneged customers may be retained in the system. Using probability generating functions (PGFs) technique, we formally obtain the steady-state solution of the proposed queueing system. Further, important performance measures and cost model are derived. Finally, numerical examples are presented

Multi-Queue Request Scheduling for Profit Maximization in IaaS Clouds

[EN] In cloud computing, service providers rent heterogeneous servers from cloud providers, i.e., Infrastructure as a Service (IaaS), to meet requests of consumers. The heterogeneity of servers and impatience of consumers pose great challenges to service providers for profit maximization. In this article, we transform this problem into a multi-queue model where the optimal expected response time of each queue is theoretically analyzed. A multi-queue request scheduling algorithm framework is proposed to maximize the total profit of service providers, which consists of three components: request stream splitting, requests allocation, and server assignment. A request stream splitting algorithm is designed to split the arriving requests to minimize the response time in the multi-queue system. An allocation algorithm, which adopts a one-step improvement strategy, is developed to further optimize the response time of the requests. Furthermore, an algorithm is developed to determine the appropriate number of required servers of each queue. After statistically calibrating parameters and algorithm components over a comprehensive set of random instances, the proposed algorithms are compared with the state-of-the-art over both simulated and real-world instances. The results indicate that the proposed multi-queue request scheduling algorithm outperforms the other algorithms with acceptable computational time.This work was supported in part by the National Key Research and Development Program of China under Grant 2017YFB1400800, in part by the National Natural Science Foundation of China under Grants 61872077 and 61832004, and in part by the Collaborative InnovationCenter of Wireless Communications Technology. The work of Quan Z. Sheng was supported in part by Australian Research Council Future Fellowship under Grant FT140101247 and in part by Discovery Project under Grant DP180102378. The work of Ruben Ruiz was supported in part by the Spanish Ministry of Science, Innovation, and Universities through the project OPTEP-Port Terminal Operations Optimization under Grant RTI2018-094940-B-I00 financed with FEDER fundsWang, S.; Li, X.; Sheng, QZ.; Ruiz García, R.; Zhang, J.; Beheshti, A. (2021). Multi-Queue Request Scheduling for Profit Maximization in IaaS Clouds. IEEE Transactions on Parallel and Distributed Systems. 32(11):2838-2851. https://doi.org/10.1109/TPDS.2021.3075254S28382851321

Stationary Analysis of a Multiserver queue with multiple working vacation and impatient customers

We consider an M/M/c queue with multiple working vacation and impatient customers. The server serves the customers at a lower rate rather than completely halts the service during this working vacation period. The impatience of the customer’s arises when they arrive during the working vacation period, where the service rate of the customer’s is lower than the normal busy period. The queue is analyzed for multiple working vacation policies. The policy of a MWV demands the server to keep taking vacation until it finds at least a single customer waiting in the system at an instant vacation completion. On returning of the server from his vacation along with finding at least one customer in the system, the server changes its service rate, thereby giving rise to a non-vacation period; otherwise the server immediately goes for another WV. We formulate the probability generating function for the number of customers present when the server is both in a service period as well as in a working vacation period. We further derive a closed-form solution for various performance measures such as the mean queue length and the mean waiting time. The stochastic decomposition properties are verified for the model