Accuracy of state space collapse for earliest-deadline-first Queues

This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems, performance is measured by the fraction of customers who meet their deadline, rather than more traditional performance measures, such as customer delay, queue length or server utilization. To model such systems, one must keep track of customer lead times (the time remaining until a customer deadline elapses) or equivalent information. This paper reviews the earlier heavy traffic analysis of such systems that provided approximations to the system's behavior. The main result of this paper is the development of a second-order analysis that gives the accuracy of the approximations and the rate of convergence of the sequence of real-time queueing systems to its heavy traffic limit.Comment: Published at http://dx.doi.org/10.1214/105051605000000809 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimizing Bandwidth Sharing for Real-time Traffic in Wireless Networks

We consider the problem of enhancing the delivery of real-time traffic in wireless networks using bandwidth sharing between operators. A key characteristic of real-time traffic is that a packet has to be delivered within a delay deadline for it to be useful. The abundance of real-time traffic is evident in the popularity of applications like video and audio conferencing, which increased significantly during the COVID-19 period. We propose a sharing and scheduling policy which involves dynamically sharing a portion of one operator's bandwidth with another operator. We provide strong theoretical guarantees for the policy. We also evaluate its performance via extensive simulations, which show significant improvements of up to 90% in the ability to carry real-time traffic when using the policy. We also explore how the improvements from bandwidth sharing depend on the amount of sharing, and on additional traffic characteristics

Random trees in queueing systems with deadlines

AbstractWe survey our research on scheduling aperiodic tasks in real-time systems in order to illustrate the benefits of modelling queueing systems by means of random trees. Relying on a discrete-time single-server queueing system, we investigated deadline meeting properties of several scheduling algorithms employed for servicing probabilistically arriving tasks, characterized by arbitrary arrival and execution time distributions and a constant service time deadline T. Taking a non-queueing theory approach (i.e., without stable-stable assumptions) we found that the probability distribution of the random time sT where such a system operates without violating any task's deadline is approximately exponential with parameter λT = 1μT, with the expectation E[sT] = μT growing exponentially in T. The value μT depends on the particular scheduling algorithm, and its derivation is based on the combinatorial and asymptotic analysis of certain random trees. This paper demonstrates that random trees provide an efficient common framework to deal with different scheduling disciplines and gives an overview of the various combinatorial and asymptotic methods used in the appropriate analysis