Abstract
The delivery of latency sensitive packets is a crucial issue in real-time applications of communication networks. Such packets often have a firm deadline and a packet becomes useless if it arrives after its deadline. The deadline, however, applies only to the packet’s journey through the entire network; individual routers along the packet’s route face a more flexible deadline. We study policies for admitting latency sensitive packets at a router. Each packet is tagged with a value. A packet waiting at a router loses value over time as its probability of arriving at its destination on time decreases. The router is modeled as a non-preemptive queue, and its objective is to maximize the total value of the forwarded packets. When a router receives a packet, it must either accept it (and delay future packets), or reject it immediately. The best policy depends on the set of values that a packet can take. We consider three natural sets: an unrestricted model, a real-valued model, where any value over 1 is allowed, and an integral-valued model. For the unrestricted model, we prove that there is no constant competitive ratio algorithm. For the real-valued model, we give a randomized 4-competitive algorithm and a matching lower bound (up to low order terms). We also provide a deterministic lower bound of \(\phi ^3 - {\varepsilon }\approx 4.236\), almost matching the previously known 4.24-competitive algorithm. For the integral-valued model, we describe a deterministic 4-competitive algorithm, and prove that this is tight even for randomized algorithms (up to low order terms).
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Notes
An oblivious adversary is familiar with ALG, but does not know the results of the actual coin tosses of ALG.
We forbid packets from arriving at integral times to simplify notation and avoid the need to decide whether a packet arriving at an integral time t can be transmitted in t (assuming the queue is empty when the packet arrives). Regardless of which decision is made, general arrival times can be easily reduced to non-integral arrival times.
Fiat et al. (2007) is a presentation given by one of the authors of Fiat et al. (2008), but never formally published. Currently, it is available in the URL address: http://www.powershow.com/view/12b46a-ZTA0M/Competitive_Queue_Management_for_Latency_Sensitive_Packets_powerpoint_ppt_presentation.
Algorithm 2 is inspired by the 5.25-competitive \({\mathsf {DT}}\) algorithm presented by Fiat et al. (2008).
The definition of \(b_{\beta , k}\) in Fiat et al. (2008) is slightly different, but both definitions use the same idea.
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Acknowledgments
The research of Joseph (Seffi) Naor was supported by ISF Grant 1366/07.
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An extended abstract of this work appeared in IEEE INFOCOM 2010.
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Feldman, M., Naor, J. Non-preemptive buffer management for latency sensitive packets. J Sched 20, 337–353 (2017). https://doi.org/10.1007/s10951-016-0474-0
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DOI: https://doi.org/10.1007/s10951-016-0474-0