Necessity of Future Information in Admission Control

Abstract

We study the necessity of predictive information in a class of queueing admission control problems, where a system manager is allowed to divert incoming jobs up to a fixed rate, in order to minimize the queueing delay experienced by the admitted jobs. Spencer et al. (2014) show that the system's delay performance can be significantly improved by having access to future information in the form of a lookahead window, during which the times of future arrivals and services are revealed. They prove that, while delay under an optimal online policy diverges to infinity in the heavy-traffic regime, it can stay bounded by making use of future information. However, the diversion polices of Spencer et al. (2014) require the length of the lookahead window to grow to infinity at a non-trivial rate in the heavy-traffic regime, and it remained open whether substantial performance improvement could still be achieved with less future information.We resolve this question to a large extent by establishing an asymptotically tight lower bound on how much future information is necessary to achieve superior performance, which matches the upper bound of Spencer et al. (2014) up to a constant multiplicative factor. Our result hence demonstrates that the system's heavy-traffic delay performance is highly sensitive to the amount of future information available. Our proof is based on analyzing certain excursion probabilities of the input sample paths, and exploiting a connection between a policy's diversion decisions and subsequent server idling, which may be of independent interest for related dynamic resource allocation problems.

Learning-aided Stochastic Network Optimization with Imperfect State Prediction

“…Then, we see from Lemma 5 that with probability 1 − O(V −3 log(V )/4 ), distribution change will be detected before t ≤ t k + d. At that time, we have γ * (t) − γ * = O(V e w ). Combining this with the fact that q(t ) = O(D k + d), we see that (21) follows. This completes the proof.…”

“…This proves (20). To prove (21), define G 1 = Θ(D k + 2 log(V ) 2 (1 + V e w )). Then, we see from Lemma 5 that with probability 1 − O(V −3 log(V )/4 ), distribution change will be detected before t ≤ t k + d. At that time, we have γ * (t) − γ * = O(V e w ).…”

Proactive Customer Service: Operational Benefits and Economic Frictions

“…More relevant is the work that considers customers who may accept product delivery early, that is, are flexible to the timing of product delivery (Karaesmen et al 2004, Wang andToktay 2008). The study of future information in the context of service as opposed to inventory systems is more limited and has focused mainly on demand-side interventions in the form of admission control (e.g, Spencer et al 2014, Xu 2015, Xu and Chan 2016. As far as we are aware, the only other work that studies proactive service is Zhang (2014).…”

Intelligence of Smart Systems: Model, Bounds, and Algorithms

“…Having established (18), we construct the following ideal algorithm by choosing pre-service actions to minimize the right-hand-side of the drift.…”

“…However, all arXiv:1605.02585v1 [math.OC] 9 May 2016 these works focus only on causal systems, i.e., service begins only after demand enters the system. Recent works [15], [16], [17], [18] and [19] consider queueing system control with future traffic demand information. Works [20] and [21] also consider similar problems where systems can proactively serve user demand.…”