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This paper is cited in the following contexts:
On the Comparison of Queueing Systems With Their Fluid Limits - Altman, Jiménez, Koole (2001) (1 citation) (Correct)
....ffl T BA(i) f(u; x) P 1 k=0 p i k f(u; x ke i ) Here we take the p i k 0 such that P 1 k=0 p i k = 1. Dene p i = P 1 k=0 kp i k . In the next section we compare V n and V B n . But let us try to understand why TBA(i) is an interesting operator to consider. It is known ([2, 15]) that any probability distribution can be approximated arbitrarily close by a mixture of Erlang or gamma distributions, all with the same parameter. With TBA(i) we can model this approximation. When we increase the accuracy of the approximation, the batch sizes increase, but the service time per ....
....arrivals converges to the AEuid model. Thus it remains to show that the batch arrival model converges to the original queueing model. As the workload at t is a continuous function of the input, it suOEces to show that G k converges to G. This result however is well known, and can be found in [15] (see also Appendix A of [7] It looks as if we have nished proving Theorem 2.4; there is one complication left however. In X B t the tasks of which a batch consists are treated separately, while they should be treated as a whole. In the current systems one task of a batch can be processed at ....
R. Schassberger. Warteschlangen. Springer-Verlag, 1973.
Aspects of RT Databases - (ed.) (Correct)
....S l , followed by path m with duration Sm . Then E[S r ] E[ S l Sm ) r ] Based on these rules, the moments of S can be found using dynamic programming. Note that the analysis produces the exact values of the moments E[S r ] 22 Chapter 1 Fitting a distribution to the moments In [15] it is proved that each positive random variable can be approximated arbitrarily well by a weighted sum of independent exponentially distributed variables. We used this result to find a mixture of exponentially distributed variables that has the same moments as S. The choice of this mixture ....
R. Schassberger. Warteschlangen. Springer Verlag, 1973.
The Response Time Distribution in a.. - Bodlaender.. (1995) (1 citation) (Correct)
.... X (r; r; X (i;j) i j=r 1 a (r; i;j) E[S 2 [i;j] 6 Approximating the response time distribution by fitting Schassberger proved that each positive stochastic variable can be approximated arbitrarily well by a weighted sum of independent exponentially distributed variables (see [Sch93]) We 0 2 4 6 8 10 0 0.05 0.1 0.15 0.2 0.25 E[S] B(1) 4 CPUs, analysis 3 CPUs, analysis 4 CPUs, simulation 3 CPUs, simulation (a) First moment 0 20 40 60 80 100 120 0 0.05 0.1 0.15 0.2 0.25 4 CPUs, analysis 3 CPUs, analysis 4 CPUs, simulation 3 CPUs, simulation (b) Second moment Figure 4: ....
R. Schassberger. Warteschlangen. Springer-Verlag, Berlin, 1993.
Modelling and Construction of Real-Time Database Schedulers - Van Der (Correct)
....] pE[S r l ] 1 Gamma p)E[S r m ] ffl Addition. The transaction first follows path l with duration S l , followed by path m with duration Sm . Then E[S r ] E[ S l Sm ) r ] Based on these rules, the moments of S can be found using dynamic programming. 2) Fitting the moments: In [Sch73] it is proved that each positive stochastic variable can be approximated arbitrarily well by a weighted sum of independent exponentially distributed variables. We used this result to find a mixture of exponentially distributed variables that has the same moments as S. The choice of this mixture ....
R. Schassberger. Warteschlangen. Springer Verlag, 1973.
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