Mathematics – Probability
Scientific paper
2006-07-03
Annals of Applied Probability 2006, Vol. 16, No. 2, 516-561
Mathematics
Probability
Published at http://dx.doi.org/10.1214/105051605000000809 in the Annals of Applied Probability (http://www.imstat.org/aap/) by
Scientific paper
10.1214/105051605000000809
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.
Kruk Łukasz
Lehoczky John
Shreve Steven
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