The Annals of Applied Probability

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

Łukasz Kruk, John Lehoczky, and Steven Shreve

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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

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

First available in Project Euclid: 29 June 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60G57: Random measures 60J65: Brownian motion [See also 58J65] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

State space collapse due dates heavy traffic queueing diffusion limits random measures


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.

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