Competitive Analysis of Constrained Queueing Systems

We consider the classical problem of constrained queueing (or switched networks): There is a set of N queues to which unit sized packets arrive. The queues are interdependent, so that at any time step, only a subset of the queues can be activated. One packet from each activated queue can be transmitted, and leaves the system. The set of feasible subsets that can be activated, denoted S, is downward closed and is known in advance. The goal is to find a scheduling policy that minimizes average delay (or flow time) of the packets. The constrained queueing problem models several practical settings including packet transmission in wireless networks and scheduling cross-bar switches. In this paper, we study this problem using the the competitive analysis: The packet arrivals can be adversarial and the scheduling policy only uses information about packets currently queued in the system. We present an online algorithm, that for any epsilon > 0, has average flow time at most O(R^2/epsilon^3*OPT+NR) when given (1+epsilon) speed, i.e., the ability to schedule (1+epsilon) packets on average per time step. Here, R is the maximum number of queues that can be simultaneously scheduled, and OPT is the average flow time of the optimal policy. This asymptotic competitive ratio O(R^3/epsilon^3) improves upon the previous O(N/epsilon^2) which was obtained in the context of multi-dimensional scheduling [Im/Kulkarni/Munagala, FOCS 2015]. In the full general model where N can be exponentially larger than R, this is an exponential improvement. The algorithm presented in this paper is based on Makespan estimates which is very different from that in [Im/Kulkarni/Munagala, FOCS 2015], a variation of the Max-Weight algorithm. Further, our policy is myopic, meaning that scheduling decisions at any step are based only on the current composition of the queues. We finally show that speed augmentation is necessary to achieve any bounded competitive ratio

Adaptive Matching for Expert Systems with Uncertain Task Types

A matching in a two-sided market often incurs an externality: a matched resource may become unavailable to the other side of the market, at least for a while. This is especially an issue in online platforms involving human experts as the expert resources are often scarce. The efficient utilization of experts in these platforms is made challenging by the fact that the information available about the parties involved is usually limited. To address this challenge, we develop a model of a task-expert matching system where a task is matched to an expert using not only the prior information about the task but also the feedback obtained from the past matches. In our model the tasks arrive online while the experts are fixed and constrained by a finite service capacity. For this model, we characterize the maximum task resolution throughput a platform can achieve. We show that the natural greedy approaches where each expert is assigned a task most suitable to her skill is suboptimal, as it does not internalize the above externality. We develop a throughput optimal backpressure algorithm which does so by accounting for the `congestion' among different task types. Finally, we validate our model and confirm our theoretical findings with data-driven simulations via logs of Math.StackExchange, a StackOverflow forum dedicated to mathematics.Comment: A part of it presented at Allerton Conference 2017, 18 page

Optimizing Your Online-Advertisement Asynchronously

We consider the problem of designing optimal online-ad investment strategies for a single advertiser, who invests at multiple sponsored search sites simultaneously, with the objective of maximizing his average revenue subject to the advertising budget constraint. A greedy online investment scheme is developed to achieve an average revenue that can be pushed to within $O(\epsilon)$ of the optimal, for any $\epsilon>0$, with a tradeoff that the temporal budget violation is $O(1/\epsilon)$. Different from many existing algorithms, our scheme allows the advertiser to \emph{asynchronously} update his investments on each search engine site, hence applies to systems where the timescales of action update intervals are heterogeneous for different sites. We also quantify the impact of inaccurate estimation of the system dynamics and show that the algorithm is robust against imperfect system knowledge

Performance analysis of a discrete-time queueing system with customer deadlines

This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the "deadline" of the customer. Deadlines of consecutive customers are modelled as independent and geometrically distributed random variables. The arrival process of new customers, furthermore, is assumed to be general and independent, while service times of the customers are deterministically equal to one slot each. For this queueing model, we are able to obtain exact formulas for quantities as the mean system content, the mean customer delay, and the deadline-expiration ratio. These formulas, however, contain infinite sums and infinite products, which implies that truncations are required to actually compute numerical values. Therefore, we also derive some easy-to-evaluate approximate results for the main performance measures. These approximate results are quite accurate, as we show in some numerical examples. Possible applications of this type of queueing model are numerous: the (variable) deadlines could model, for instance, the fact that customers may become impatient and leave the queue unserved if they have to wait too long in line, but they could also reflect the fact that the service of a customer is not useful anymore if it cannot be delivered soon enough, etc

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

Stability conditions for a decentralised medium access algorithm: single- and multi-hop networks

We consider a decentralised multi-access algorithm, motivated primarily by the control of transmissions in a wireless network. For a finite single-hop network with arbitrary interference constraints we prove stochastic stability under the natural conditions. For infinite and finite single-hop networks, we obtain broad rate-stability conditions. We also consider symmetric finite multi-hop networks and show that the natural condition is sufficient for stochastic stability