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  • 1
    Electronic Resource
    Electronic Resource
    On pathwise behavior of multiserver queues (1994)
    Springer
    Queueing systems 15 (1994), S. 279-288 
    Details
    ISSN: 1572-9443
    Keywords: Sample-path ; point processes ; workload ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, by exploiting recent results on the pathwise behavior of the workload process in single server, work conserving queues of theG/G/1/∞ type, we show that the workload of multiserver, work conserving queues ofG/G/m/∞ (m〈∞) (andG/G/∞) queues satisfies an o(t) growth condition, provided that the time average of the work brought into the system is less thanm form 〈 ∞ (and finite form=∞).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189241
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  • 2
    Electronic Resource
    Electronic Resource
    On the capability of the policing function to release an ATM connection (1993)
    Springer
    Telecommunication systems 2 (1993), S. 239-259 
    Details
    ISSN: 1572-9451
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The capability of releasing a connection has been recognized within standardization bodies as a desirable feature for the policing function in ATM networks. In this paper, we investigate how to implement this new scheme. For this purpose, we introduce a simple modification to some well known policing mechanisms, namely the Leaky Bucket, the EWMA, the Jumping and Moving Window. We first draw attention to the fact that all of them suffer from the drawback that they discard useful information which could be used to enforce tighter policing and to shut a connection off when too much excess traffic is submitted to the connection. We then propose a modification to the above mentioned schemes in which the discarded cell information is used, with almost no overhead compared to the usual ones. In the context of the Leaky Bucket, analysis using Bernoulli and On/Off MMBP input processes shows that the modified version has a behavior which differs significantly from its original counterpart. A major difference is that the new mechanism stops serving sources requiring much more resources than negotiated. It also reacts more severely to abuses of smaller magnitude and polices the sources closer to their declared resource utilization. A method is then presented to select the appropriate parameters of the modified Leaky Bucket in order to achieve a faster response time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02109860
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  • 3
    Electronic Resource
    Electronic Resource
    Asymptotic results for the superposition of a large number of data connections on an ATM link (1997)
    Springer
    Queueing systems 26 (1997), S. 121-150 
    Details
    ISSN: 1572-9443
    Keywords: ATM ; statistical multiplexing ; M/PH/∞ ; queueing system ; transient characteristics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The M/PH/∞ system is introduced in this paper to analyze the superposition of a large number of data connections on an ATM link. In this model, information is transmitted in bursts of data arriving at the link as a Poisson process of rate λ and burst durations are PH distributed with unit mean. Some transient characteristics of the M/PH/∞ system, namely the duration θ of an excursion by the occupation process {Xt} above the link transmission capacity C, the area V swept under process {Xt} above C and the number of customers arriving in such an excursion period, are introduced as performance measures. Explicit methods of computing their distributions are described. It is then shown that, as conjectured in earlier studies, random variables Cθ,CV and N converge in distribution as C tends to infinity while the utilization factor of the link defined by γ = λ/C is fixed in (0,1), towards some transient characteristics of an M/M/1 queue with input rate γ and unit service rate. Further simulation results show that after adjustment of the load of the M/M/1 queue, a similar convergence result holds for the superposition of a large number of On/Off sources with various On and Off period distributions. This shows that some transient quantities associated with an M/M/1 queue can be used in the characterization of open loop multiplexing of a large number of On/Off sources on an ATM link.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019172922497
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  • 4
    Electronic Resource
    Electronic Resource
    On the area swept under the occupation process of an M/M/1 queue in a busy period (1998)
    Springer
    Queueing systems 29 (1998), S. 383-398 
    Details
    ISSN: 1572-9443
    Keywords: M/M/1 queue ; continued fractions ; Bessel functions ; asymptotic expansion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We compute in this paper the distribution of the area $$\mathcal{A}$$ swept under the occupation process of an M/M/1 queue during a busy period. For this purpose, we use the expression of the Laplace transform $${\mathcal{A}^ \star }$$ of the random variable $$\mathcal{A}$$ established in earlier studies as a fraction of Bessel functions. To get information on the poles and the residues of $${\mathcal{A}^ \star }$$ , we take benefit of the fact that this function can be represented by a continued fraction. We then show that this continued fraction is the even part of an S fraction and we identify its successive denominators by means of Lommel polynomials. This allows us to numerically evaluate the poles and the residues. Numerical evidence shows that the poles are very close to the numbers $$\sigma _n = - \left( {1 + \rho } \right)/n$$ as $$n \to \infty$$ . This motivated us to formulate some conjectures, which lead to the derivation of the asymptotic behaviour of the poles and the residues. This is finally used to derive the asymptotic behaviour of the probability survivor function $$P\left\{{\mathcal{A}〉x}\right\}$$ . The outstanding property of the random variable $$\mathcal{A}$$ is that the poles accumulate at 0 and its tail does not exhibit a nice exponential decay but a decay of the form $$cx^{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-\nulldelimiterspace} 2}} {\text{e}}^{ - \gamma \sqrt x }$$ for some positive constants c and $$\gamma$$ , which indicates that the random variable $${\mathcal{A}}$$ has a Weibull-like tail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019100617896
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  • 5
    Electronic Resource
    Electronic Resource
    Simulation‐based results of weighted fair queuing algorithms for ATM networks (1999)
    Springer
    Telecommunication systems 12 (1999), S. 149-166 
    Details
    ISSN: 1572-9451
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The behavior of the ideal General Processor Sharing (GPS) discipline and different per‐VC queuing algorithms approximating this ideal scheme, namely the Self Clocked Fair Queuing, the Packet by Packet Generalized Processor Sharing, and the Virtual Starting Time disciplines, are studied in this paper via simulation. We specifically consider a simple simulation configuration involving two Constant Bit rate (CBR) connections and several ON/OFF connections (bursty traffic). This simple simulation experiment allows us to point out three important features of the GPS and approximating disciplines. First, by adequately choosing the weight coefficients, these scheduling schemes can offer to CBR traffic almost Head of Line (HOL) priority over ON/OFF connections, to each of which, nevertheless, a minimum bandwidth is guaranteed. Second, GPS and per‐VC queuing disciplines, like the simple FIFO scheme, is very sensitive to burst scale congestion phenomena. Finally, simulation results seem to indicate that the scheduling disciplines considered perform traffic shaping on ON/OFF connections, which drastically reduces the burstiness of output traffic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019142611787
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  • 6
    Electronic Resource
    Electronic Resource
    On a random variable associated with excursions in an M/M/∞ system (1999)
    Springer
    Queueing systems 32 (1999), S. 305-318 
    Details
    ISSN: 1572-9443
    Keywords: M/M/∞ system ; excursions ; continued fractions ; Laplace transform ; Stieltjes transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We show in this paper how the theory of continued fractions can be used to invert the Laplace transform of a transient characteristic associated with excursions in an M/M/∞ system with unit service rate and input intensity u. The characteristic under consideration is the area V swept under the occupation process of an M/M/∞ queue during an excursion period above a given threshold C. The Laplace transform V ⋆ of this random variable has been established in earlier studies and can be expressed as a ratio of Tricomi functions. In this paper, we first establish the continued fraction representation of V ⋆, which allows us to obtain an alternative expression of the Laplace transform in terms of Kummer functions. It then turns out that the continued fraction considered is the even part of a Stieltjes (S) fraction, which provides information on the location of the poles of V ⋆. It appears that the Laplace transform has simple poles on the real negative axis. Taking benefit of the fact that the spectrum is compact and that the numerical values of the Laplace transform can easily be computed by means of the continued fraction, we finally use a classical Laplace transform inversion technique to numerically compute the survivor probability distribution function x➙ℙ{V 〉 fx} of the random variable V, which exhibits an exponential decay only for very large values of the argument x when the ratio u/C is sufficiently smaller than one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019199306934
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