Linus E. Schrage and Louis W. Miller. The queue M/G/1 with the shortest remaining processing time discipline. Operations Research, 14:670--684, 1966.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....penalized) by SRPT scheduling. These new theoretical results have motivated us to reconsider unfair scheduling. It s not immediately clear what SRPT means in the context of a Web server. The SRPT scheduling policy is well understood in the context of a single queue, single resource system [27]: at any moment in time, give the full resource to that one request with the shortest remaining processing time requirement. However a Web server is not a single resource system; thus it would be highly inefficient to schedule only one request at a time to run in the Web server. Furthermore, it is ....

Linus E. Schrage and Louis W. Miller. The queue M/G/1 with the shortest remaining processing time discipline. Operations Research, 14:670--684, 1966.

....penalized) by SRPT scheduling. These new theoretical results have motivated us to reconsider unfair scheduling. It s not immediately clear what SRPT means in the context of a Web server. The SRPT scheduling policy is well understood in the context of a single queue, single resource system [27]: at any moment in time, give the full resource to that one request with the shortest remaining processing time requirement. However a Web server is not a single resource system; thus it would be highly inefficient to schedule only one request at a time to run in the Web server. Furthermore, it is ....

Linus E. Schrage and Louis W. Miller. The queue M/G/1 with the shortest remaining processing time discipline. Operations Research, 14:670--684, 1966.

....cantly worse than SRPT with respect to mean slowdown. At the end of our paper (Section 6) we turn to analysis for insight into the behavior of the shortestconnection rst scheduling policy. In that section we examine a single queue under SRPT scheduling, which was analyzed by Schrage and Miller [18]. In addition to scheduling theory, our work also touches on issues of OS architecture. In particular, the work we describe in this paper helps to expose de ciencies in traditional operating system structure that prevent precise implementation of service policies like shortest connection rst. ....

....in both cases, tasks with small remaining processing time are always given preference over tasks with longer remaining processing time. Our analytical results throughout are based on the following equation for the mean response time for a task of size x in an M=G=1 queue with load , under SRPT [18]: EfR SRPT x g = R x 0 t 2 dF (t) x 2 (1 F (x) 2 1 R x 0 t dF (t) 2 Z x 0 1 (1 ( R t 0 z dF (z) dt where R x is the response time (departure time minus arrival time) of a job of size x, F ( is the cumulative distribution function of service time, and is ....

Linus E. Schrage and Louis W. Miller. The queue M/G/1 with the shortest remaining processing time discipline. Operations Research, 14:670-684, 1966.

....Remaining Processing Time (SRPT) policy is optimal over all uniprocessor policies [2,14] As a result, R Psi max(S; R 1 SRPT ) 8 Psi 2 Pi: We use the superscript 1 to denote that the policy is a uniprocessor policy. For Poisson job arrivals we can compute R 1 SRPT from the analysis in [13]. The SRPT policy uses complete knowledge of job demands. If only restricted job demand information is available to the scheduler, e.g. policies in Pi 0 . we can obtain a tighter bound. First consider cases where fD i g 1 i=1 are i.i.d. and independent of everything else. If D i has an ....

SCHRAGE, L. The queue M/G/1 with the shortest remaining processing time discipline. Oper. Res. 14, 4 (1966), 670-684.

....Remaining Processing Time (SRPT) policy is optimal over all uniprocessor policies [2,14] As a result, R Psi max(S; R 1 SRPT ) 8 Psi 2 Pi: We use the superscript 1 to denote that the policy is a uniprocessor policy. For Poisson job arrivals we can compute R 1 SRPT from the analysis in [13]. The SRPT policy uses complete knowledge of job demands. We can obtain tighter bounds if only restricted job demand information is available to the scheduler, e.g. policies in Pi 0 . First consider cases where fD i g 1 i=1 are i.i.d. and independent of everything else. If D i has an ....

SCHRAGE, L. The queue M/G/1 with the shortest remaining processing time discipline. Oper. Res. 14, 4 (1966), 670-684.

....the potential performance improvements that are possible if SRPT scheduling is used in the context of our model of a Web server. Our analytical results throughout this paper are based on the following formulas for the mean flow time for a task of size x, for an M G 1 queue with load ae under SRPT[15] and under PS[12] EfFlowtime for a task of size x under SRPTg = EfWaiting time for task of size xg EfResidence time of a task of size xg = R x 0 t 2 dF (t) x 2 (1 Gamma F (x) 2 (1 Gamma R x 0 tdF (t) 2 Z x 0 1 (1 Gamma ( R t 0 zdF (z) dt EfFlowtime for a task of ....

Linus E. Schrage and Louis W. Miller. The queue m=g=1 with the shortest remaining processing time discipline. Operations Research, 14:670--684, 1966.

....with respect to mean slowdown. At the end of our paper (Section 6) we turn to analysis for insight into the behavior of the shortest connection first and size independent scheduling policies. In that section we examine a single queue under SRPT scheduling, which was analyzed by Schrage and Miller [19], and compare it with a simple queue under processor sharing scheduling, which was analyzed by Kleinrock [16] In addition to scheduling theory, our work also touches on issues of OS architecture. In particular, the work we describe in this paper helps to expose deficiencies in traditional ....

....in both cases, tasks with small remaining processing time are always given preference over tasks with longer remaining processing time. Our analytical results throughout are based on the following equations for the mean response time for a task of size x in an M=G=1 queue with load ae, under SRPT [19] and under PS [16] EfR SRPT x g = R x 0 t 2 dF (t) x 2 (1 Gamma F (x) 2 (1 Gamma R x 0 t dF (t) 2 Z x 0 1 (1 Gamma ( R t 0 z dF (z) dt EfR PS x g = x 1 Gamma ae where R x is the response time (departure time minus arrival time) of a job of size x, F ( Delta) ....

Linus E. Schrage and Louis W. Miller. The queue M/G/1 with the shortest remaining processing time discipline. Operations Research, 14:670--684, 1966.

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