Browsing by Subject "Markovian arrival process"

Now showing 1 - 4 of 4

Open Access
A numerically efficient method for the MAP/D/1/K queue via rational approximations
(Springer New York LLC, 1996-03) Akar, N.; Arıkan, E.
The Markovian Arrival Process (MAP), which contains the Markov Modulated Poisson Process (MMPP) and the Phase-Type (PH) renewal processes as special cases, is a convenient traffic model for use in the performance analysis of Asynchronous Transfer Mode (ATM) networks. In ATM networks, packets are of fixed length and the buffering memory in switching nodes is limited to a finite numberK of cells. These motivate us to study the MAP/D/1/K queue. We present an algorithm to compute the stationary virtual waiting time distribution for the MAP/D/1/K queue via rational approximations for the deterministic service time distribution in transform domain. These approximations include the well-known Erlang distributions and the Padé approximations that we propose. Using these approximations, the solution for the queueing system is shown to reduce to the solution of a linear differential equation with suitable boundary conditions. The proposed algorithm has a computational complexity independent of the queue storage capacityK. We show through numerical examples that, the idea of using Padé approximations for the MAP/D/1/K queue can yield very high accuracy with tractable computational load even in the case of large queue capacities.
Open Access
Performance study of asynchronous/ synchronous optical burst/ packet switching with partial wavelength conversion
(2006) Doğan, Kaan
Wavelength conversion is known to be one of the most effective methods for contention resolution in optical packet/burst switching networks. In this thesis, we study various optical switch architectures that employ partial wavelength conversion, as opposed to full wavelength conversion, in which a number of converters are statistically shared per input or output link. Blocking is inevitable in case contention cannot be resolved and the probability of packet blocking is key to performance studies surrounding optical packet switching systems. For asynchronous switching systems with per output link converter sharing, a robust and scalable Markovian queueing model has recently been proposed by Akar and Karasan for calculating blocking probabilities in case of Poisson traffic. One of the main contributions of this thesis is that this existing model has been extended to cover the more general case of a Markovian arrival process through which one can study the impact of traffic parameters on system performance. We further study the same problem but with the converters being of limited range type. Although an analytical model is hard to build for this problem, we show through simulations that the so-called far conversion policy in which the optical packet is switched onto the farthest available wavelength in the tuning range, outperforms the other policies we studied. We point out the clustering effect in the use of wavelengths to explain this phenomenon. Finally, we study a synchronous optical packet switching architecture employing partial wavelength conversion at the input using the per input line converter sharing. For this architecture, we first obtain the optimal wavelength scheduler using integer linear programming and then we propose a number of heuristical scheduling algorithms. These algorithms are tested using simulations under symmetric and asymmetric traffic scenarios. Our results demonstrate that one can substantially reduce the costs of converters used in optical switching systems by using share per input link converter sharing without having to sacrifice much from the low blocking probabilities provided by full input wavelength conversion. Moreover, we show that the heuristic algorithm that we propose in this paper provides packet loss probabilities very close to those achievable using integer linear programming and is also easy to implement.
Open Access
Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials
(Applied Probability Trust, 2016) Dayar T.; Orhan, M. C.
A multiclass c-server retrial queueing system in which customers arrive according to a class-dependent Markovian arrival process (MAP) is considered. Service and retrial times follow class-dependent phase-type (PH) distributions with the further assumption that PH distributions of retrial times are acyclic. A necessary and sufficient condition for ergodicity is obtained from criteria based on drifts. The infinite state space of the model is truncated with an appropriately chosen Lyapunov function. The truncated model is described as a multidimensional Markov chain, and a Kronecker representation of its generator matrix is numerically analyzed.
Open Access
The workload-dependent MAP/PH/1 queue with infinite/finite workload capacity
(Elsevier, 2013) Yazici, M. A.; Akar, N.
We propose a numerical algorithm for finding the steady-state queue occupancy distribution for a workload-dependent MAP/PH/1 queue in which the arrival process and the service rate depend continuously on the instantaneous workload in the system. Both infinite and finite queue capacity scenarios are considered, including partial rejection and complete rejection policies for the latter. Using discretization, this system is approximately described by a multi-regime Markov fluid queue for which numerical algorithms are available. The computational complexity of the proposed method is linear in the number of regimes used for discretization. We provide numerical examples to validate the proposed approach.