K. De Turck

Performance of the IEEE 802.16e Sleep Mode Mechanism in the Presence of Bidirectional Traffic

We refine existing performance studies of the WiMAX sleep mode operation to take into account uplink as well as downlink traffic. This as opposed to previous studies which neglected the influence of uplink traffic. We obtain numerically efficient procedures to compute both delay and energy efficiency characteristics. A test scenario with an Individual Subscriber Internet traffic model in both directions shows that even a small amount of uplink traffic has a profound effect on the system performance.

Markov-modulated Ornstein-Uhlenbeck processes

Abstract In this paper we consider an Ornstein–Uhlenbeck (OU) process (M(t))t≥0 whose parameters are determined by an external Markov process (X(t))t≥0 on a finite state space {1, . . ., d}; this process is usually referred to as Markov-modulated Ornstein–Uhlenbeck. We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a system of partial differential equations (PDEs) for the Laplace transform of M(t) and the state X(t) of the background process, jointly for time epochs t = t1, . . ., tK. Then we use this PDE to set up a recursion that yields all moments of M(t) and its stationary counterpart; we also find an expression for the covariance between M(t) and M(t + u). We then establish a functional central limit theorem for M(t) for the situation that certain parameters of the underlying OU processes are scaled, in combination with the modulating Markov process being accelerated; interestingly, specific scalings lead to drastically different limiting processes. We conclude the paper by considering the situation of a single Markov process modulating multiple OU processes.

Large deviations of an infinite-server system with a linearly scaled background process

Abstract This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates λ i by a factor N and the transition rates ν i j of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where N tends to ∞ ). The paper also presents qualitative properties of the system’s behavior conditional on the rare event under consideration happening.

Markovian SIR model for opinion propagation

In this work, we propose a new model for the dynamics of single opinion propagation at a size-limited location with a low population turnover. This means that a maximum number of individuals can be supported by the location and that the allowed individuals have a long sojourn time before leaving the location. The individuals can have either no opinion (S), a strong opinion that they want to spread (I), or an opinion that they keep for themselves (R); the letters stem from the popular Susceptible-Infectious-Recovered (SIR) epidemic model. Furthermore, we consider a variable opinion transmission rate. Hence, the opinion spreading is modelled as a Markovian non-standard SIR epidemic model with stochastic arrivals, departures, infections and recoveries. We evaluate the system performance by two complementary approaches: we apply a numerical but approximate solution approach which relies on Maclaurin series expansions and we investigate the fluid limit of the system at hand. Finally, we illustrate our approach by some numerical examples.

Stability of multiwavelength optical buffers with delay‐oriented scheduling

This contribution presents the first stability analysis of multiwavelength queueing systems. Results are obtained for a wide class of implementable scheduling disciplines referred to as delay-oriented disciplines, a class to which for example join the shortest queue belongs. Scheduling is applied as contention resolution in optical switches accommodated with fibre delay lines as means of buffering. The analysis yields sufficient stability conditions for multiwavelength optical buffers with a general fibre-delay-line set, renewal input and general service times. Copyright

Performance analysis of a kitting process as a paired queue

Nowadays, customers request more variation in a company’s product assortment leading to an increased amount of parts moving around on the shop floor. To cope with this tendency, a kitting process can be implemented. Kitting is the operation of collecting the necessary parts for a given end product in a specific container, called a kit, prior to arriving at an assembly unit. As kitting performance is critical to the overall cost and performance of the manufacturing system, this paper analyses a two-part kitting process as a Markovian model. In particular, kitting is studied as a paired queue, thereby accounting for stochastic part arrivals, and kit assembly times. Using sparse matrix techniques, we assess the impact of kitting interruptions, bursty part arrivals and phase-type distributed kit assembly times on the behaviour of the part buffers. Finally, a cost-profit analysis of kitting processes is conducted and an approximation for a two-part kitting process is established.

Performance analysis of a decoupling stock in a Make-to-Order system

Abstract In a Make-to-Order system, products are only manufactured when orders are placed. As this may lead to overly long delivery times, a stock of semi-finished products can be installed to reduce production time: the so-called decoupling stock. As performance of the decoupling stock is critical to the overall performance and cost of the production system, we propose and analyse a Markovian model of the decoupling stock. In particular, we focus on a queueing model with two buffers, thereby accounting for both the decoupling stock as well as for possible backlog of orders. By means of numerical examples, we then quantify the impact of production inefficiency on delivery times and overall cost.

Optimized Channel and Delay Selection for Contention Resolution in Optical Networks

Both optical packet switching and optical burst switching provide viable alternatives to the current electronic switching in the backbone. To resolve contention, contiguous packets/bursts are sent over different channels, and/or provided with different Fiber Delay Line (FDL) buffer delays. Typically, the resulting channel and delay selection (CDS) algorithm bases its decision on the horizon value of the different channels. Up to now, a horizon algorithm known as MING (MINimal Gap) was assumed to provide minimal loss. Relying on Markov chain-based performance modeling and a Markov decision process (MDP), we reexamine the optimality of MING. This enables us to construct CDS algorithms that outperform MING, and this for any buffer size, traffic load and packet/burst size distribution. Further, we consider burst-size-dependent and load-dependent scheduling, two stochastic mechanisms that, together with preventive dropping, enhance the algorithms performance. The paper presents the developed method in detail, together with detailed results of the performance gain realized.

Rare-event analysis of modulated OrnsteinUhlenbeck processes

This paper studies OrnsteinUhlenbeck (OU) processes in a random environment. The OU model has found widespread use in networking, as a Gaussian approximation of the user-level dynamics that allows explicit analysis; adding modulation to it allows incorporating phenomena in which the users activity level is affected by exogenous factors. The focus lies on rare-event analysis: under a specific scaling of the parameters involved, we establish the large deviations asymptotics of the probability that the process reaches an extreme value. The decay rate of this probability is generally only implicitly available (as the solution to a variational problem), but specializing to the case of Markov modulation we succeed in devising efficient numerical procedures.

On the impact of the sensing rate of secondary users in Cognitive Radio Networks

The first phase in the operation of a Cognitive Radio Network (CRN) is the investigation of the availability of idle channels through channel sensing. In this paper we study the impact of the sensing rate of Secondary Users (SUs) in a CRN. We develop a continuous-time Markov chain (CTMC) to study the effect of the sensing rate σ on the performance measures of the CRN including the expected SU delay, the SU interruption probability, the probability a SU is discarded after entering the system and the SU blocking probability. The obtained results reveal that the sensing rate has a crucial impact on these measures.