The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 16, Number 2 (2006), 516-561.
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.
Ann. Appl. Probab., Volume 16, Number 2 (2006), 516-561.
First available in Project Euclid: 29 June 2006
Permanent link to this document
Digital Object Identifier
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]
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