Scheduling Co-Reservations with Priorities in Grid Computing Systems Rui Min and Muthucumaru Maheswaran Advanced Networking Research Laboratory Department of Computer Science University of Manitoba Winnipeg, MB R3T 2N2, Canada Email: ruimin@ee, maheswar@cs .umanitoba.ca This paper presents three algorithms for co-reserving re- sources. A novel mechanism for specifying QoS constraints with the requests is introduced. The performance of the al- gorithms are studied through extensive simulations. The re- sults indicate that depending on the objective of optimiza- tion different algorithms should be used. One of the distin- guishing features of our algorithms is that they operate in a pseudo-online mode (called the “batch” mode). 1. Introduction Advance resource reservations and co-reservations in the context of Grid computing have been the focus of few stud- ies [1, 2]. Algorithms for supporting advance reservations in high-performance computing environments are presented in [2]. These algorithms treat reservation requests and re- quests for resources from “batch” jobs in a unified manner and they allow users to request multiple resources simulta- neously (i.e., perform co-reservations). However, [2] does not allow different users to “space share” the resources dur- ing the same time intervals. Further, the batch applications are assumed to have lower priority than the reservation re- quests. Another system for performing co-reservation in Grid systems is the Globus Architecture for Reservation and Allocation (GARA) [1]. This paper proposes algorithms for scheduling co- reservations on heterogeneous resources. Although, only CPU resources are considered here, the approach may be generalized to other resources such as network and storage. Further, in this paper, immediate reservations are modeled as advance reservations with current time as the start time and a predefined length of time for the duration. This allows us to unify advance and immediate reservations. The Co-reservation Scheduler with Priorities and Bene- fit functions (Co-RSPB) presented here considers the rela- tive priorities of the different reservation requests. In Co- RSPB, each request has an associated benefit function that quantifies the “profit” accrued by the client by securing the resource at the requested level. When a client is willing to negotiate for lower service levels, it could indicate this by This research was partially supported by a Natural Sciences and Engineer- ing Research Council of Canada Grant RGP 220278 and equipment used was provided by a Canada Foundation for Innovation grant. providing a benefit function that shows a reduced but posi- tive benefit. 2. Co-Reservation Algorithms and Evaluation The algorithms are based on the following assumptions. Once a request is granted reservation, a contract for the reservation is signed between the application and the sys- tem. The co-reservation scheduler won’t examine the same request more than once except when a QoS violation occurs. In this study, each co-reservation request involves multiple resources. If any one required resource is not available to the application, the overall request will be rejected by the reservation scheduler. All three algorithms assemble a meta-request by accu- mulating several reservation requests. The meta-request is then scheduled by the chosen heuristic. A request is referred to as floating if any resource set can satisfy the request and called fixed, otherwise. The Co-RSPB, schedules the float- ing requests as follows. The requests in the meta-request are sorted by the priority and the requests are considered in de- scending order by the priority. Because the requests are co- reservation requests, they can have sub-requests. The sub- requests are sorted by the minimum CPU requirement and are considered for allocation in descending order by min- imum CPU requirement. In the Co-reservation scheduler with Best Fit Scheme (Co-RSBF), the requests are sorted by the sum of the sub-requests’ CPU requirements. The rest of the Co-RSBF algorithm is same as the Co-RSPB algo- rithm. The Co-reservation scheduler with Best Fit and Re- fining (Co-RSBFR) algorithm uses the Co-RSBF algorithm and admits the reservation requests and increases the benefit delivered to the requests via the refinement process. Simulations were performed to evaluate the performance of the different co-reservation algorithms. Figure 1 shows the variation of system benefit and the number of rejections with the number of requests. Figure 2 shows the variation of system benefit with the number of machines. Figure 3 shows the variation of the number of rejections with the av- erage of duration. The lower system benefit provided by Co-RSBF can be explained by noting that Co-RSBF selects the reservation that provides the applications the lowest possible benefit even when there is no resource scarcity. Although Co-RSBF Proceedings of the 2nd IEEE/ACM International Symposium on Cluster Computing and the Grid (CCGRID02) 0-7695-1582-7/02 $17.00 ' 2002 IEEE