This paper uses submodularity to obtain monotonicity results for a class of Markovian queueing network service rate control problems. Nonlinear costs of queueing and service are allowed. In contrast to Weber and Stidham [14], our monotonicity theorem considers arbitrary directions in the state space (not just control directions), arrival routing problems, and certain uncontrolled service rates....

One of the most important performance measures in the analysis of data networks is the average delay required to deliver a packet from origin to destination. The packet delay will aaect the choice and performance of several network algorithms such as routing and ow control. Queueing theory is the primary methodological framework for analyzing network delay. It provides a basis for adequate dela...

This paper studies the instability of multiclass queueing networks. We prove that if a uid limit model of the queueing network is weakly unstable, then the queueing network is unstable in the sense that the total number of customers in the queueing network diverges to innnity with probability one as time t ! 1. Our result provides a converse to a recent result of Dai 2] which states that a queu...

Fair queueing has long been a popular paradigm for providing bounded delay channel access and separation between ows in wireline networks. However, adapting fair queueing to the wireless domain is non-trivial because of the unique problems in wireless channels such as location-dependent and bursty channel error. In this article, we identify the key issues in wireless fair queueing, deene a wire...

We consider a queueing model with finite capacities. External arrivals follow a Coxian distribution. Due to the limitation of the capacity, arrivals may be lost if the buffer is full. Our goal is to study the probability of blocking. In order to obtain the steady-state probability distribution of this model, we construct an embedded Markov chain at the departure points. The solution is solved ...

Queueing network models have been widely applied for performance modeling and analysis of computer networks. Queueing network models with finite capacity queues and blocking (QNB) allow representing and analyzing systems with finite resources and population constraints. Different protocols can be defined to deal with finite capacity resources and they can be modeled in queueing networks with bl...

For non-trivial (open) queueing networks and also for tandem queueing networks, de omposition often represents the only feasible solution method besides simulation. The network is partitioned into individual nodes whi h are analyzed in isolation with respe t to approximate internal traÆ representations. The quality of the qui kly obtainable results very mu h depends on the des riptors for the t...

Queueing networks are an adequate model type for the analysis of complex system behavior. Most of the more realistic models are rather complex and do not fall into the easy solvable class of product form networks. Those models have to be analyzed by numerical solution of the underlying Markov chain and/or approximation techniques including simulation. In this paper a class of hierarchically str...

A b s t r a c t Queueing network models with finite capacity queues and blocking are used to represent systems with finite capacity resources and with resource constraints, such as production, communication and computer systems. Various blocking mechanisms have been defined in literature to represent the various behaviours of real systems with limited resources. Queueing networks with finite ca...

1 Introduction Queueing networks constitute a large family of models in a variety of settings, involving " jobs " or " customers " that wait in queues until being served. Once its service is completed, a job moves to the next prescribed queue, where it remains until being served. This procedure continues until the job leaves the network; jobs also enter the network according to some assigned ru...