Roland de Haan

A Tandem Queueing Model for Delay Analysis in Disconnected Ad Hoc Networks

Ad hoc network routing protocols may fail to operate in the absence of an end-to-end connection from source to destination. This deficiency can be resolved by so-called delay-tolerant networking which exploits the mobility of the nodes by letting them operate as relays according to the store-carry-and-forward paradigm. In this work, we analyze the delay performance of a small mobile ad hoc network by considering a tandem queueing system. We present an exact packet-level analysis by applying ideas from the polling literature. Due to the state-space expansion, this analysis cannot efficiently be applied for all model parameter settings. For this reason, an analytical approximation is constructed and its excellent performance has extensively been validated. Numerical results on the mean end-to-end delay show that the switch-over time distribution impacts this metric only through its first two moments. Finally, we study delay optimization under power control.

Time-limited polling systems with batch arrivals and phase-type service times

In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the queue becomes empty, whichever occurs first. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling systems. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-lengths at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains.

Time-limited and k-limited polling systems: a matrix analytic solution

In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time.

Delay in a tandem queueing model with mobile queues: An analytical approximation

In this paper, we analyze the end-to-end delay performance of a tandem queueing system with mobile queues. Due to state-space explosion, there is no hope for a numerical exact analysis for the joint-queue-length distribution. For this reason, we present an analytical approximation that is based on queue-length analysis. Through extensive numerical validation, we find that the queue-length approximation exhibits excellent performance for light traffic load.