## The Annals of Applied Probability

### Accuracy of state space collapse for earliest-deadline-first queues

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 16, Number 2 (2006), 516-561.

Dates
First available in Project Euclid: 29 June 2006

https://projecteuclid.org/euclid.aoap/1151592242

Digital Object Identifier
doi:10.1214/105051605000000809

Mathematical Reviews number (MathSciNet)
MR2244424

Zentralblatt MATH identifier
1129.60084

#### Citation

Kruk, Łukasz; Lehoczky, John; Shreve, Steven. Accuracy of state space collapse for earliest-deadline-first queues. Ann. Appl. Probab. 16 (2006), no. 2, 516--561. doi:10.1214/105051605000000809. https://projecteuclid.org/euclid.aoap/1151592242

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