Thomas Demoor

Mixed Finite-/Infinite-Capacity Priority Queue with Interclass Correlation

We consider a discrete-time queueing system with two priority classes and absolute priority scheduling. In our model, we capture potential correlation between the arrivals of the two priority classes. For practical use, it is required that the high-priority queue is of (relatively) small size and we hence use a model with finite high-priority queue capacity. We obtain expressions for the probability mass functions of the steady-state system content and delay of the high-priority class as well as for the probability generating functions and moments of the steady-state system content and delay of the low-priority class. The results are compared to those of a similar system, but with an infinite capacity for high priority packets, and it is shown that the latter can be inaccurate. We also investigate the effect of correlation between the arrivals of both priority classes on the performance of the system.

The preemptive repeat hybrid server interruption model

We analyze a discrete-time queueing system with server interruptions and a hybrid preemptive repeat interruption discipline. Such a discipline encapsulates both the preemptive repeat identical and the preemptive repeat different disciplines. By the introduction and analysis of so-called service completion times, we significantly reduce the complexity of the analysis. Our results include a.o. the probability generating functions and moments of queue content and delay. Finally, by means of some numerical examples, we assess how performance measures are affected by the specifics of the interruption discipline.

Analytic evaluation of power saving in cooperative communication

This paper addresses the effects of power saving mechanisms on cooperation in wireless networks. Cooperation by relaying data of other wireless nodes is crucial in (next-generation) wireless networks as it can greatly attribute to ensuring connectivity, reliability, performance, etc. As power saving relies on sleep mode, turning off the communication subsystem for predetermined amounts of time, it can greatly affect data relaying as a cooperator node may not be awake when there is data to relay. Rather than modelling one of the wireless protocols in detail, we construct a high-level queuing model capturing the two essential characteristics of cooperation and energy efficiency: relaying and sleep mode. The used analytical approach allows for accurate performance evaluation and enables us to investigate the trade-off between data relaying and energy efficiency.

On the effect of combining cooperative communication with sleep mode

Cooperation is crucial in (next-generation) wireless networks as it can greatly attribute to ensuring connectivity, reliability, performance, ... Relaying looks promising in a wide variety of network types (cellular, ad-hoc on-demand), each using a certain protocol. Energy efficiency constitutes another key aspect of such networks, as battery power is often limited, and is typically achieved by sleep mode operation. As the range of applications is very broad, rather than modelling one of the protocols in detail, we construct a high-level model capturing the two essential characteristics of cooperation and energy efficiency: relaying and sleep mode, and study their interaction. The used analytical approach allows for accurate performance evaluation and enables us to unveil less trivial trade-offs and to formulate rules-of-thumb applicable across all potential scenarios.

Modelling queue sizes in an expedited forwarding DiffServ router with service differentiation

This paper studies a single-server non-preemptive priority queue with two traffic classes in order to model Expedited Forwarding Per-Hop Behaviour in the Differentiated Services (DiffServ) architecture. Generally, queueing models assume infinite queue capacity but in a DiffServ router the capacity for high priority traffic is typically small to prevent this traffic from monopolizing the output link and hence causing starvation of low-priority traffic. The presented model takes the exact (finite) high-priority queue capacity into account. Analytical formulas for the system content of each class are determined as well as the high-priority packet loss ratio. For each class, service of a packet takes a (different) general independent distribution. The issues this causes are resolved by using the spectral decomposition theorem. Numerical examples indicate the considerable impact of the finite capacity on the system performance.

Time and space priority in a partially shared priority queue

This paper studies a finite-sized discrete-time priority queue. Arriving packets can be classified into two types: delay-sensitive (class-1) packets and loss-sensitive (class-2) packets. Packets of both classes arrive according to a two-class discrete batch Markovian arrival process (2-DBMAP), taking into account the correlated nature of arrivals in heterogeneous telecommunication networks. Packets of class 1 have absolute transmission priority over class-2 packets whereas the latter receive space priority as the partial buffer sharing acceptance policy is used. The concurrent use of time and space priority, each for different packets, raises some issues on the order of arrivals in a slot. This is resolved by adopting a string representation for sequences of arriving packets and by defining a probability measure on the set of such strings. Performance of this queueing system is then determined using matrix-analytic techniques. Finally, the impact of various system parameters is demonstrated in several numerical examples.

Mixed Finite-/Infinite-Capacity Priority Queue with General Class-1 Service Times

This paper studies a single-server queue with two traffic classes in order to model Expedited Forwarding Per-Hop Behaviour in the Differentiated Services architecture. Generally, queueing models assume infinite queue capacity but in a DiffServ router the capacity for high priority traffic is often small to prevent this traffic from monopolizing the output link and hence causing starvation of other traffic. The presented model takes the exact (finite) high-priority queue capacity into account. Analytical formulas for system contents and packet delay of each traffic class are determined. This requires extensive use of the spectral decomposition theorem as the service time of a high-priority packet takes a general distribution, which complicates the analysis. Numerical examples indicate the considerable impact of the finite capacity on the system performance.

Uncovering the evolution from finite to infinite high-priority capacity in a priority queue

Infinite capacity queues are often used as approximation for their finite real-world counterparts as they are mathematically tractable. It is generally known that tail probabilities of low-priority system content in a two-class priority queue with infinite capacity for customers of both priority classes can be non-exponential, even if the interarrival time and service time distributions are exponentially decaying. In contrast, when the capacity for the high-priority customers is finite, tail probabilities of low-priority system content are always exponentially decaying. Therefore, using the results for one as an (accurate) approximation for the other is not obvious. From an analytical point of view, the non-exponentiality in the infinite case is caused by the arisal of an implicitly defined function, a root of the kernel, in the probability generating function for the low-priority system content. However, up till now, it has been unclear how this non-exponentiality suddenly emerges when taking the limit from to the finite to the infinite case. Our main contribution is that, under the restriction of a maximum of two arrivals per slot, a recurrence relation in the high-priority capacity is constructed resulting in an explicit expression for the corresponding generating function for the finite case. Amazingly, this expression contains all roots of the kernel in the infinite case. Taking the limit of this expression leads to the well-known behavior for the infinite case as the root inside the complex unit circle dominates the other roots uncovering the evolution from the finite to the infinite case. Furthermore, we investigate under which circumstances the standard tail characterizations are inaccurate.