COHEN, J. W. (1994). On the effective bandwidth in buffer design for the multi-server channels. Technical report, CWI Report BS-R9406, NL-1090 GB, Amsterdam, The Netherlends.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....QOS parameter (performance measure) for this queueing system is the buffer occupancy probability distribution. The problem of multiplexing dates back to [RUB73, COH74] In [COH74] Cohen obtained a complete Laplace transform solution to this problem (More recently, he revisited this problem in [COH94]. However, inverting the Laplace transform is usually a very tedious process. Hence, investigating computationally tractable exact and approximate solution techniques are needed. For Markovian (fluid) On Off processes a thorough investigation of this problem was done in [AMS82] Many other ....

J. W. Cohen, "On the effective bandwidth in buffer design for the multi-server channels," Technical report, CWI Report BS-R9406, 1994.

....of other more smoothly operating sources, it is already most interesting to study the case of one such badly behaved source. The paper is organized as follows. The fluid queueing system under consideration is described in Section 2. Section 3 displays for this model some key results of Cohen [9] that form the starting point of our approach. Section 4 considers the case that sources 2; N all have a negative exponential activity period distribution, while Section 5 considers the more general case that sources 2; N have activity period distributions with an exponential tail ....

....with mean 1= j , and the activity periods A ij have distribution A j ( Delta) with A j (0 ) 0 and with mean ff j and Laplace Stieltjes Transform (LST) ff j ( Delta) We assume that r j 1, j = 1; N . This assumption is restrictive and can be relaxed (see Section 6, and also Section 5 of [9]) we hope to discuss this issue in more detail in a future study. The total traffic load offered to the buffer per unit time is assumed to be less than one: L : N X j=1 r j ff j j 1 ff j j 1: 2.1) This is the ergodicity condition, cf. 9] 3. The fluid queue Let V t denote the ....

[Article contains additional citation context not shown here]

J.W. Cohen (1994). On the effective bandwidth in buffer design for the multi-server channels, CWI Report BS-R9406.

....server queue with multiplexed On Off arrivals gives us the most basic understanding of contention. Mathematical investigation of this problem dates back to [94, 33] In [33] Cohen obtained a complete Laplace transform solution to this problem (More recently, he 97 revisited this problem in [34]. However, inverting the Laplace transform is usually a very tedious process. Hence, investigating computationally tractable exact and approximate solution techniques are needed. For Markovian (fluid) On Off sources, a thorough investigation of this problem was done in [3] Many other results for ....

J. W. Cohen. On the effective bandwidth in buffer design for the multi-server channels. Technical report, CWI Report BS-R9406, 1994.

....case: E [P i: ae i i (1 Gamma ae) 1 if ae = 1) i = 1; 2; E [P : ae (1 Gamma ae) Remark 3.5 ffl In [15] uniqueness had only been proved among solutions that are Laplace Stieltjes transforms. ffl Condition ae 1 is the ergodicity condition of the buffer content process, cf. [10]. 11 Proof of Theorem 3.4: The right hand side of (10) is obtained by integrating formula (9) with z = 0) with respect to y according to the distribution of A 11 (and similarly for source 2) To prove that the system of equations (10) admits a unique solution, we first construct a minimal ....

J.W. Cohen. On the effective bandwidth in buffer design for the multiserver channels. Report BS-R9406, CWI, 1994.

....results and bounds are mentioned in Subsection 4.4 for the case of several sources with long tailed on period distributions. 4. 1 Characteristics of the global, fluid source The description of the global source is originally due to Cohen [15] and has been recently completed by the same author [17]. Here we adopt the convention that all the sources are initially silent. 4. Superposition of on off sources 20 If I i (t) denotes the indicator function of fsource i silent at time tg, then I(t) Q N i=1 I i (t) is the analogous indicator for the global source. Now set: h i (t) r i Z t ....

.... to: E[e Gamma W ] 1 Gamma fi 1 Gamma fiE[e Gamma B 1 ] Gamma (1 Gamma fi) Gamma (1 Gamma E[e Gamma B 1 ] Such an extension is justified by Cohen in the case when all the Laplace Stieltjes transforms ff i [ 1 i N , have negative abscissae of convergence [17]; but this means that all the active periods A i1 , 1 i N , have exponential moments, which we will precisely not assume in the sequel. We will later see however that the extension can still be justified when all the sources but one have exponentially tailed active periods. Also notice the ....

[Article contains additional citation context not shown here]

J.W. Cohen. On the effective bandwidth in buffer design for the multi-server channels. Report BS-R9406, CWI, 1994.

....result that the tail of the buffer content distribution is Weibullian. They also indicate how their model relates to that of Norros. Our paper is organized as follows. The fluid queueing system under consideration is described in Section 2. Section 3 displays for this model some key results of [7, 9] that form the starting point of our approach. Section 4 summarizes the main ingredients of the theory of regular variation. Our results are gathered in Sections 5 7. Section 5 considers the case of a single on off source. We show that, analogously to the ordinary GI G 1 queue, the buffer content ....

....1= j , and the activity periods A ij have distribution A j ( Delta) with A j (0 ) 0 and with mean ff j and Laplace Stieltjes Transform (LST) ff j ( Delta) We assume that r j 1, j = 1; N . This assumption is somewhat restrictive and can be relaxed (see Remark 6. 2 and also Section 5 of [9]) we shall discuss this issue in more detail in a future study. The total traffic load offered to the buffer per unit time is assumed to be less than one: L : N X j=1 r j ff j j 1 ff j j 1: 2.1) This is the ergodicity condition, cf. 9] 3. The fluid queue Let V t denote the ....

[Article contains additional citation context not shown here]

J.W. Cohen (1994). On the effective bandwidth in buffer design for the multi-server channels, CWI Report BS-R9406.

....ae i i (1 Gamma ae) i = 1; 2; E [P : ae (1 Gamma ae) with the convention 1=0 = 1) Remark 3.5 ffl In [16] uniqueness had only been proved among solutions that are Laplace Stieltjes transforms. ffl Condition ae 1 is the ergodicity condition of the buffer content process, cf. [10]. Proof of Theorem 3.4: The right hand side of (3.6) is obtained by integrating formula (3.5) with z = 0) with respect to y according to the distribution of A11 (and similarly for source 2) To prove that the system of equations (3.6) admits a unique solution, we first construct a minimal ....

Cohen, J. W. On the effective bandwidth in buffer design for the multi-server channels. Report BS-R9406, CWI, 1994.

....QOS parameter (performance measure) for this queueing system is the buffer occupancy probability distribution. The problem of multiplexing dates back to [RUB73, COH74] In [COH74] Cohen obtained a complete Laplace transform solution to this problem (More recently, he revisited this problem in [COH94]. However, inverting the Laplace transform is usually a very tedious process. Hence, investigating computationally tractable exact and approximate solution techniques are needed. For Markovian (fluid) On Off processes a thorough investigation of this problem was done in [AMS82] Many other ....

J. W. Cohen, "On the effective bandwidth in buffer design for the multi-server channels," Technical report, CWI Report BS-R9406, 1994.

....arrivals; the main QOS parameter (performance measure) for this queueing system is the buffer overflow probability distribution. This problem dates back to [RUB73, COH74] In [COH74] Cohen obtained a complete Laplace transform solution to this problem (More recently, he revisited this problem in [COH94]. However, inverting the Laplace transform is usually a very tedious process. Hence, investigating computationally tractable exact and approximate solution techniques are needed. For Markovian (fluid) On Off sources, a thorough investigation of this problem was done in [AMS82] Many other results ....

J. W. Cohen, "On the effective bandwidth in buffer design for the multi-server channels," Technical report, CWI Report BS-R9406, 1994.

....The quantitative analysis of a single server queue with multiplexed On Off arrivals gives us the most basic understanding of contention. This problem dates back to [37, 14] In [14] Cohen obtained a complete Laplace transform solution to this problem (More recently, he revisited this problem in [15]. However, inverting the Laplace transform is usually a very tedious process. Hence, investigating computationally tractable exact and approximate solution techniques are needed. For Markovian (fluid) On Off sources, a thorough investigation of this problem was done in [2] Many other results for ....

J. W. Cohen. On the effective bandwidth in buffer design for the multi-server channels. Technical report, CWI Report BS-R9406, 1994.

No context found.

COHEN, J. W. (1994). On the effective bandwidth in buffer design for the multi-server channels. Technical report, CWI Report BS-R9406, NL-1090 GB, Amsterdam, The Netherlends.

No context found.

Cohen, J. W. (1995). On the effective bandwidth in buffer design for the multi-server channels. Technical Report BS-R9406, Department of Operations Research, Statistics, and System Theory, Centrum voor Wiskunde en Informatica (CWI), Amsterdam.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC