W. Fischer and K. Meier-Hellstern, "The Markovmodulated Poisson process (MMPP) cookbook," Performance Evaluation, vol. 18, no 2, pp. 149-171, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....between packet losses from an exponential distribution with a median calculated from the observed data. The sojoum time of the loss state was calculated from the 85 CDF of the intmburst loss data. This model is a Markov Modulated Poisson Process (MMPP) MMPPs are described in detail in Fischer [FiHe1992]. Altman [A1AvBA2000] found that losses on a wide area network are best modeled with a Poisson loss process based on a Markov Arrival Process, of which MMPP is a subset. 5.2.3 Implementing the MMPP model in ns2 The ns2 simulator supports a k state Markov error model with the MultiState loss ....

W. Fischer, K. Meier-Hellstem, "The Markov-modulated Poisson Process (MMPP) Cookbook ", Performance Evaluation, Vol 18, 1992.

....up of batches of independent identically distributed batch sizes (i.e. number of simultaneous arrivals in a batch) independent identically distributed inter batch intervals, and the batch sizes are also independent from the inter batch intervals. Markov Modulated Poisson Process (MMPP) models [4, 5, 21] have become very popular traffic models over the last years. An MMPP consists of a Poisson process whose rate is controlled by the state of a Markov process. In our study we use a 2 state MMPP. 2.3 Overflow and aggregation models We considered an overflow model (OVER) to model the traffic which ....

W. Fischer, K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook", Performance Evaluation 18 (1992) 149-171, North-Holland. Ext. 22/6

....up of batches of independent identically distributed batch sizes (i.e. number of simultaneous arrivals in a batch) independent identically distributed inter batch intervals, and the batch sizes are also independent from the inter batch intervals. Markov Modulated Poisson Process (MMPP) models [3, 4, 18] have become very popular traffic models over the last years. An MMPP consists of a Poisson process whose rate is controlled by the state of a Markov process. In our study we use a 2 state MMPP. 2.3 Overflow and aggregation models We considered an overflow model (OVER) to model the traffic which ....

W. Fischer, K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook", Performance Evaluation 18 (1992) 149-171, North-Holland.

....probability by the model after the burst arrives, but a high probability before the burst) Maintaining the traffic model during traffic arrivals is the task of state estimation. In our initial work in this framework, we have used Markov modulated Bernoulli Process (MMBP) traffic models (e.g. [7], 14] These models can easily represent a wide variety of interesting traffic patterns, including self similar traffic. An MMBP traffic model is a discrete time model given by providing a finite set S of traffic generation states, with a transition probability matrix T giving for each pair of ....

W. Fischer and K. Meier-Hellstern, "The Markovmodulated Poisson process (MMPP) cookbook," Perf. Evaluation, Vol. 18, pp. 149--171, 1992.

.... [125] and extended by Lucantoni [109] and subsume many familiar arrival processes as special cases (e.g. Markov Modulated Poisson Processes (MMPP) and phase type renewal processes [109] and have been used for network traffic characterization (see, for example, Fischer and Meier Hellstern [53] and Blondia [19] MAP models can also approximate self similar traffic sources arbitrarily well (see, for example, 4, 5, 119] Here, we will use the equivalent term Hidden Markov Model (HMM) instead of MAP to emphasize the fact that the server cannot access the state information of the MAP, but ....

W. Fischer and K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook," Performance Evaluation, vol. 18, pp. 149--171, 1992.

....a low probability by the model after the burst arrives, but a high probability before the burst) Maintaining the tra#c model during tra#c arrivals is the task of state estimation. In our initial work in this framework, we have used Markov modulated Bernoulli Process (MMBP) tra#c models (e.g. [7], 14] These models can easily represent a wide variety of interesting tra#c patterns, including self similar tra#c. An MMBP tra#c model is a discrete time model given by providing a finite set S of tra#c generation states, with a transition probability matrix T giving for each pair of states s ....

W. Fischer and K. Meier-Hellstern, "The Markovmodulated Poisson process (MMPP) cookbook," Perf. Evaluation, Vol. 18, pp. 149--171, 1992.

.... for computing the response time distribution of a statistical multiplexer being fed by a Markovian Modulated Process (MMP) pioneered by Neuts [51] see, in particular, the important work by Regterschot and de Smit on the M G 1 queue with Markov modulated arrivals and services [55] as well as [27] for a recent survey of this area) Unfortunately, these computations are typically very expensive and do not easily yield the tail probability distribution. Consequently, there has been considerable interest in the development of approximations. These include methods which approximate the arrival ....

....Section 3.5 concludes with numerical results and a discussion on the tightness of the various bounds presented in Sections 3.2 3.4. 3. 1 Bounds for Queues in Markovian Environment We assume that customers arrive at a FIFO single server queue according to a Markov modulated Poisson process (t n ) n [27]. More precisely, we assume that the arrival process is a doubly stochastic Poisson process with arrival rate Z(t) at time t, where (Z(t) t 0) is an irreducible Markov process on the set S = f1; 2; Kg, with infinitesimal generator Q = q ij ] rate matrix = diag ( 1 ; K ) and ....

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W. Fischer and K. Meier-Hellstern, "The Markov-Modulated Poisson Process (MMPP) Cookbook ", Perf. Evaluation, 18, pp. 149--172, 1992.

....network. Previous work in this area falls into three categories. First, a considerable amount of work has focussed on the development of algorithms for computing the response time distribution of a statistical multiplexer being fed by a Markovian Arrival Process (MAP) pioneered by Neuts [31] see[14] for a recent survey of this area) Unfortunately, these computations are typically very expensive. Consequently, there has been considerable interest in the development of bounds on performance for very general arrival processes. This is exemplified by the works of Cruz [6, 7] Kurose [28] ....

....the queue is fed by N independent MMAP s (A j n (Y j n ) n , j = 1; 2; N . Let S j be the (finite) state space of the aperiodic, irreducible, homogeneous Markov chain (Y j n ) n , and denote by P j = j p kl ] its transition matrix and by j its invariant measure. It is known (cf. [14] for instance) that the superposition of N such independent Markov modulated processes is again a Markov modulated process (A n (Y n ) n , where Y n is an aperiodic, irreducible, homogeneous Markov chain on the states S = Q N j=1 S j with transition matrix P and invariant measure given by P = ....

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W. Fischer and K. Meier-Hellstern, "The Markov-Modulated Poisson Process (MMPP) Cookbook ", Perf. Evaluation, 18, pp. 149-172, 1992.

....set Sm with transition matrix Pm and stationary distribution m , and where (U m n (k) n is a renewal process for fixed m and k. We further assume that the Markov chains (Y m n ) n (1 m M) and the renewal processes (U m n (k) k 2 Sm , 1 m M) are mutually independent. It is worth noting [9] that the aggregate arrival process (A n ) n is also a MMAP with state space S = Q M m=1 Sm , underlying Markov chain (Y n ) n = Y 1 n ; Y M n ) n , transition matrix P = Omega M m=1 Pm , and stationary distribution = Omega M m=1 m m, where Omega denotes the Kronecker product. ....

W. Fischer and K. Meier-Hellstern, "The Markov-Modulated Poisson Process (MMPP) Cookbook", Perf. Evaluation, 18, 149 -- 172, 1992.

....per port will be 0.5 and is derived exactly as before. Thus the moments of the service times are obtained exactly like in the previous section using Eqns 1 7. The first and second moments of the packet delays in the input queue can now be obtained using well known techniques for MMPP G 1 queues [6]. The procedure is summarised in the appendix. Numerical results are obtained as follows. We use the Bellcore traces [10] and derive their statistical properties in terms of the Hurst parameter, the correlation at lag 1 and the time scales over which the burstiness occurs. These parameters and ....

....up of the switch. For CIOQ switches, our model gives the delay at the input buffer. The delay at the output buffer can be modeled separately. APPENDIX I. DELAY MOMENTS IN AN MMPP G 1 QUEUE The mean and second moment of the packet delay at input i, D i and D 2 i respectively, are given by [6] D i = 1 X i i w v Gamma 1 2 X 2 i i D 2 i = 1 X i i w (2) v Gamma X 3 i i 3 Gamma D i X 2 i i (16) where w v = 1 2(1 Gamma X i i ) h 2X i i X 2 i i Gamma 2X i ( 1 Gamma X i i )g i X i Phi i R i ) Q i e i Phi i ) Gamma1 r i w ....

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W. Fischer and K. Meier-Hellstern, "The Markov modulated Poisson process (MMPP) cookbook," Performance Evaluation, vol. 18, no. 2, pp. 149171, 1993.

....performance (e.g. cell loss rate and average waiting times) that can be quite optimistic. To provide more accurate results, several modeling frameworks have been recently developed among which, two have received considerable attention, namely; the Markov modulated Poisson process (MMPP) approach [6, 4, 21], and the Fluid Flow approach [1, 7, 3, 15] An MMPP is a doubly stochastic Poisson process whose arrival rate is a random variable which is modulated (i.e. controlled) by the state of a continuous time Markov chain (see [4] for details of the properties of MMPP) The MMPP traffic model is ....

.... namely; the Markov modulated Poisson process (MMPP) approach [6, 4, 21] and the Fluid Flow approach [1, 7, 3, 15] An MMPP is a doubly stochastic Poisson process whose arrival rate is a random variable which is modulated (i.e. controlled) by the state of a continuous time Markov chain (see [4] for details of the properties of MMPP) The MMPP traffic model is suitable to approximate the aggregate arrival process of computer data sources. Its major advantage is that it captures some of the important correlations between packet (i.e. cell) arrivals while remaining analytically tractable. ....

W. Fischer and K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook ", in Performance Evaluation Journal, vol. 18, pp. 149-171, 1993.

....the arrival process of these overhead packets is correlated with the on periods of Class 2 traffic. In this analysis, we assume that the two arrival processes are independent. Furthermore, instead of solving a two priority queueing model, we will use the shadow server approximation proposed in [9] to analyze two priority queues. In this approximation, we will aggregate the high priority traffic by appropriately modifying the service time of the Class 2 requests. This can be done by multiplying the service rate of data packets by (1 Gamma U o ) where U o is the utilization of the server by ....

W. Fischer and K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook, " Performance Evaluation 18, pp.149-171, 1992.

....sections, but first the traffic model is described. 5. 1 Traffic Model The input traffic streams are modeled with independent Markov Modulated Poisson Processes (MMPPs) The MMPP is used in a wide variety of applications due to their ability to capture the bursty nature of network traffic [6]. For the purpose of this paper a two state MMPP as shown in Figure 2 is used. l l 1 2 2 1 q q 1 2 2 1 T4 T3 P1 T2 T1 P2 Two state MMPP Petri Net Model Figure 2: Traffic Model The Petri net configuration for the traffic model is also shown in Figure 2 and corresponds to the MMPP if firing rates ....

Fischer, W. and Meier-Hellstern, K., "The Markov-Modulated Poisson Process (MMPP) Cookbook," Performance Evaluation, Vol. 18, No. 2, 1992, pp. 149--171.

....with each other via an unspecified connection network, incurring in a deterministic communication latency. We have assumed exponentially distributed task service times with unit average value (S = 1) As far as task arrivals at nodes are concerned, we used both Poisson arrivals and IPP arrivals [7] (to model burst workload) In addition to processing tasks, each node also has to process messages related to the broker algorithm, and to do some small amount of work to handle tickets (no additional communication is required by the ticket al..gorithm) Each protocol message requires some ....

....system workload is an interrupted Poisson process (IPP) applied in each node of the system. An IPP is a Poisson process which is alternately turned on for an exponentially distributed length of time (with mean T on ) and then turned off an other exponentially distributed time (with mean T off ) [7]. For our simulations we have chosen the IPP total period (T p = T on T off ) to be 1000 times the mean task service time S and the IPP on generation rate on = Delta, being Delta = T on = T on T off ) the average IPP duty cycle. This way the average generation rate per node is still ....

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W.Fischer and K.Meire-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook ", Performance Evaluation North-Holland, Vol 18, No 2, pp 149-171, 1993.

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W. Fischer and K. Meier-Hellstern, "The Markovmodulated Poisson process (MMPP) cookbook," Performance Evaluation, vol. 18, no 2, pp. 149-171, 1993.

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W. Fischer and K. Meier-Hellstern, "The markov-modulated poisson process MMPP cookbook, " Performance Evaluation, vol. 18, no. 2, pp. 149--171, 1992.

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Fischer, W. and Meier-Hellstern, K. (1992). The markovmodulated poisson process MMPP cookbook. Performance Evaluation, 18(2):149--171.

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W. Fischer and K. Meier-Hellstern, "The markov-modulated poisson process (MMPP) cookbook," Performance Evaluation, vol. 18, no. 2, pp. 149--171, 1993.

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W. Fischer and K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook", Performance Evaluation, Vol 18, pp 149-171, 1992.

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W. Fischer and K. Meier-Hellstren, "The Markov-modulated Poisson Process (MMPP) cookbook," Perf. Eval., vol. 18, pp. 149--171, 1992.

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W. Fischer and K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook," Performance Evaluation, Vol. 18, 1992, pp. 149-171.

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W. Fischer and K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook", Performance Evaluation, Vol 18, pp 149-171, 1992.

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W. Fischer and K. Meier-Hellstern, "The Markov-modulated Poisson process (MMPP) cookbook," Performance Evaluation, vol. 18, pp. 149-- 171, 1992.

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W. Fischer and K. Meier-Hellstern, "The Markovmodulated Poisson process (MMPP) cookbook," Perf. Eval., vol. 18, pp. 149--171, 1992.

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W. Fischer and K. Meier-Hellstern, "The Markovmodulated Poisson process (MMPP) cookbook," Performance Evaluation, vol. 18, no 2, pp. 149-171, 1993.

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Fischer, W. and Meier-Hellstern K. (1992), "The Markov-modulated Poisson process (MMPP) cookbook," Performance Evaluation, 18, 149-171.

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