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a b s t r a c tWe 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.

We present a new numerical method to obtain the finite-and infinite-horizon ruin probabilities for a general continuous-time risk problem. We assume the claim arrivals are modeled by the versatile Markovian arrival process, the claim sizes are PH-distributed, and the premium rate is allowed to depend on the instantaneous risk reserve in a piecewise-constant manner driven by a number of thresholds, i.e., multi-threshold premiums. We introduce a novel sample path technique by which the ruin problems are shown to reduce to the steadystate solution of a certain multi-regime Markov fluid queue. We propose to use the already existing numerically efficient and stable numerical algorithms for such Markov fluid queues. Numerical results are presented to validate the effectiveness of the proposed method regarding the computation of the finite-and infinite-horizon ruin probabilities for risk models including those with relatively large number of thresholds.

Abstract-Conventional multi-rate IEEE 802.11 Wireless LANs (WLANs) are associated with the so-called performance anomaly to describe the phenomenon of high bit rate nodes being dragged down by slower nodes. This anomaly is known to be an impediment to obtaining high cumulative throughputs despite the employment of effective link adaptation mechanisms. To cope with the performance anomaly, air-time fairness has been proposed as an alternative to throughput fairness, the latter being a main characteristic of the IEEE 802.11 Distributed Coordination Function (DCF). In this paper, we propose a novel distributed air-time fair MAC (Medium Access Control) without having to change the operation of the conventional DCF. In the proposed MAC, each node in the system runs multiple instances of the conventional DCF back-off algorithm where the number of DCF instances for the nodes can be chosen in a distributed manner. Both analytical and simulation-based results are provided to validate the effectiveness of the proposed air-time fair MAC.

We present an exact analytical model for singlewavelength quality of service (QoS) differentiation in a two-class optical packet switch. In this system, QoS differentiation is achieved by limiting the set of fiber delay lines (FDLs) to the low-priority class, whereas the high-priority class is allowed to access the entire FDL bank. The analytical model is based on multi-regime Markov fluid queues and is extensible to multi-class systems with more than two classes. Markovian arrival process packet arrivals and phasetype distributed packet sizes are considered for the purpose of generality. The proposed analytical model is validated through simulations. The numerical results provide insight into determining appropriate subsets of FDLs allowed for the access of the low-priority class. The results also show that it is possible to direct almost all the packet losses to the low-priority class under moderate loads.

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Optical Burst Switching (OBS) has been proposed as a candidate technology for the next-generation Internet. In OBS, packets are assembled into a burst, and a burst control packet is sent in advance to inform and reserve resources at the optical nodes in the path of the burst. In this study, we analyze the horizon-based reservation scheme in OBS using Markov fluid queues. First, we provide a solution to continuous feedback Markov fluid queues, then we model the horizon-based reservation scheme as a continuous feedback Markov fluid queue and numerically study it. We provide numerical examples to validate our model and its solution technique as well as to obtain some insight on the horizon-based reservation mechanism. © 2013 IEEE

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