Abstract
This paper investigates the online scheduling problem on parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service (GoS) levels. Hence each job and machine are labeled with the GoS levels, and each job can be processed by a particular machine only when the GoS level of the job is not less than that of the machine. The goal is to minimize the makespan. In this paper, we consider the problem with two GoS levels. It assumes that the GoS levels of the first k machines and the last m−k machines are 1 and 2, respectively. And every job has a GoS level of 1 alternatively or 2. We first prove the lower bound of the problem under consideration is at least 2. Then we discuss the performance of algorithm AW presented in Azar et al. (J. Algorithms 18:221–237, 1995) for the problem and show it has a tight bound of 4−1/m. Finally, we present an approximation algorithm with competitive ratio \(\frac{12+4\sqrt{2}}{7}\approx 2.522\) .
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Azar Y, Naor J, Rom R (1995) The competitiveness of on-line assignments. J Algorithms 18:221–237
Bar-Noy A, Freund A, Naor J (2001) On-line load balancing in a hierarchical server topology. SIAM J Comput 31:527–549
Crescenzi P, Gambosi G, Penna P (2004) On-line algorithms for the channel assignment problem in cellular networks. Discret Appl Math 137(3):237–266
Hwang H, Chang S, Lee K (2004) Parallel machine scheduling under a grade of service provision. Comput Oper Res 31:2055–2061
Jiang YW, He Y, Tang CM (2006) Optimal online algorithms for scheduling on two identical machines under a grade of service. J Zhejiang Univ Sci 7(3):309–314
Lenstra JK, Shmoys DB, Tardos NE (1990) Approximation algorithms for scheduling unrelated parallel machines. Math Program 46:259–271
Park J, Chang SY, Lee K (2006) Online and semi-online scheduling of two machines under a grade of service provision. Oper Res Lett 34(6):692–696
Zhou P, Jiang YW, He Y (2007) Parallel machines scheduling with two GoS levels. Appl Math J Chin Univ Ser A 22(3):275–284 (in Chinese)
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Research supported by Natural Science Foundation of Zhejiang Province (Y605316) and its preliminary version appeared in Proceedings of AAIM2006, LNCS, 4041, 11-21.
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Jiang, Y. Online scheduling on parallel machines with two GoS levels. J Comb Optim 16, 28–38 (2008). https://doi.org/10.1007/s10878-007-9095-z
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DOI: https://doi.org/10.1007/s10878-007-9095-z