We model the scheduling of emerging wireless data services as a Markov decision process. These services are characterized by real-time downlink data transfers such as those needed for personalized traffic, weather and business updates. Characterizing each differing service by its own time-criticality as well as reward and penalty values, we can numerically compute an optimal Markov decision scheduling rule for serving these requests. These computations suggest that we can formulate a simple near optimal rule for scheduling these services efficiently.

We formulate and analyze a model of voice and data burst traffic for cellular digital packet data (CDPD). To develop a tractible model, we make some reasonable simplifying assumptions to model the voice traffic and one of the logical CDPD channels as an M/M/1 queue in a random environment. Rather than explicitly solve the resulting matrix quadratic equation, we develop an asymptotic analysis that gives us simple approximate formulas (with error bounds) for many performance measures of interest. In particular, one metric that we highlight comes from using our approximate mean data burst delay formula to characterize the performance of a set of interacting logical CDPD channels. We do so by describing it in terms of an equivalent number of independent, dedicated CDPD channels, We can use this metric to suggest what the optimal number of logical CDPD channels for a given system should be.

The authors introduce a deterministic fluid model and two stochastic traffic models for wireless networks. The setting is a highway with multiple entrances and exits. Vehicles are classified as calling or non-calling, depending on whether they have calls in progress. The deterministic model ignores the behavior of individual vehicles and treats them as a continuous fluid, whereas the stochastic traffic models consider the random behavior of each vehicle. However, all three model's use the same two coupled partial (or ordinary) differential equations to describe the system evolution. The call density and call handoff rate (or their expected values in the stochastic models) are readily computable by solving these equations. Numerical examples are presented to illustrate how the models can be used to investigate various aspects of time and space dynamics in wireless networks. These examples also show that the models can serve as useful tools for system engineering and planning.>

Introduces a deterministic fluid model and two stochastic traffic models for wireless networks. The setting is a highway with multiple entrances and exits. Vehicles are classified as calling or noncalling, depending upon whether or not they have calls in progress. The main interest is in the calling vehicles; but noncalling vehicles are important because they can become calling vehicles if they initiate (place or receive) a call. The deterministic model ignores the behavior of individual vehicles and treats them as a continuous fluid, whereas the stochastic traffic models consider the random behavior of each vehicle. However, all three models use the same two coupled partial differential equations (PDEs) or ordinary differential equations (ODEs) to describe the evolution of the system. The call density and call handoff rate (or their expected values in the stochastic models) are readily computable by solving these equations. Since no capacity constraints are imposed in the models, these computed quantities can be regarded as offered traffic loads. The models complement each other, because the fluid model can be extended to include additional features such as capacity constraints and the interdependence between velocity and vehicular density, while the stochastic traffic model can provide probability distributions. Numerical examples are presented to illustrate how the models can be used to investigate various aspects of time and space dynamics in wireless networks.>

In this paper the class of acyclic fork-join queuing networks that arise in various applications, including parallel processing and flexible manufacturing are studied. In such queuing networks, a fork describes the simultaneous creation of several new customers, which are sent to different queues. The corresponding join occurs when the services of all these new customers are completed. The evolution equations that govern the behavior of such networks are derived. From this, the stability conditions are obtained and upper and lower bounds on the network response times are developed. These bounds are based on various stochastic ordering principles and on the notion of association of random variables.

In Gray, Homan, Obermarck, and Korth [GHOK], the authors give many conjectures based on simulation for the probabilistic analysis of transaction lock-waits and transaction deadlocks. In this paper, we introduce a probabilistic model to explain their observations.