Required service rate for mixed traffic

В данной работе нами получены границы для скорости обслуживания при некоторых ограничениях на характеристики обслуживания в неоднородной модели входящего трафика, основанной на сумме независимых фрактального броуновского движения и симметричного $\alpha$-устойчивого движения Леви с разными коэффициентами Херста $H_1$ и $H_2=1/\alpha$. Хорошо известно, что для процессов, приращения которых имеют тяжёлые хвосты, методы расчета эффективной пропускной способности, основанные на производящей функции моментов входящего потока, не применимы. Однако существуют простые соотношения между характеристиками потока, скоростью обслуживания $C$ и вероятностями $\varepsilon(b)$ переполнения для конечного и бесконечного буфера, из которых при фиксированном значении $\varepsilon(b)$ можно выразить $C$. In this paper we analyse the nonhomogenous traffic model based on sum of independent Fractional Brownian motion and symmetric $\alpha$-stable Levy process with different Hurst exponents $H_1$ and $H_2=1/\alpha$ and present bounds for the required service rate under QoS constraints. It is well known that for the processes with long-tailed increments effective bandwidths are not expressed by means of the moment generating function of the input flow. However we can derive simple relations between the flow parameters, service rate $C$ and overflow probabilities $\varepsilon (b)$ for finite and infinite buffer. In this way it is possible to find required service rate $C$ under a constraint on maximum overflow probability.

Large deviations for a feed-forward network

We consider a feed-forward network with a single-server station serving jobs with multiple levels of priority. The service discipline is preemptive in that the server always serves a job with the current highest level of priority. For this system with discontinuous dynamics, we establish the sample path large deviation principle using a weak convergence argument. In the special case where jobs have two different levels of priority, we also explicitly identify the exponential decay rate of the total population overflow probabilities by examining the geometry of the zero-level sets of the system Hamiltonians.

Large deviations for a feed-forward network

We consider a feed-forward network with a single-server station serving jobs with multiple levels of priority. The service discipline is preemptive in that the server always serves a job with the current highest level of priority. For this system with discontinuous dynamics, we establish the sample path large deviation principle using a weak convergence argument. In the special case where jobs have two different levels of priority, we also explicitly identify the exponential decay rate of the total population overflow probabilities by examining the geometry of the zero-level sets of the system Hamiltonians.

One approach in evaluating the overflow probability using the infinite fluid-flow queue

If it is going to have practical significance, the evaluation of overflow probabilities must be (1) precise, (2) computationally stable and (3) real time compatible. The existing approximation expressions are gotten by using the traditional fluid-flow analytic techniques, which are mostly based on spectral analysis. The limitation of this approach comes from numerical difficulties caries by the spectral approach. In this paper, we suggested a fluid-flow approach in evaluating the overflow probability, which fully satisfies the above stated criteria, and removes the numerical difficulties of existing methods. The authors approach is based on the renewal argument and exploiting the similarity between fluid queues and Quasi-Birth-and-Death (QBD) processes.