No abstract

Abstract-We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based (2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g. average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. We will refer to such tiebreaking rule as myopic. (3) We derive the growth rates of the number of users in the system in overload settings under various policies, which give additional insights on the performance. (4) We conclude that simple priority-index policies with the myopic tie-breaking rule, are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.

We investigate the problem of sharing the resources of a single server with time-varying capacity with the objective of minimizing the mean delay. We formulate the resource allocation problem as a Markov Decision Process. The problem is not solvable analytically in full generality, and we thus set out to obtain an approximate solution. In our main contribution, we extend the framework of multi-armed bandits to develop a heuristic solution of index type. At every given time, the heuristic assigns an index to every user that depends solely on its current state, and serves the user with highest current index value. We show that in the case of constant capacity, the heuristic policy is equivalent to the so-called Gittins index rule, which is known to be optimal under the assumption of constant capacity.

We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based [9], Proportionally Best [1] or Potential Improvement [4] are stable under the maximum stability conditions, whereas Relative-Best [10] or the cµ-rule are not. (2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g. average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. In particular, we show that simple priority-index policies with a myopic tie-breaking rule, are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.

We consider a resource allocation problem, where a rational agent has to decide how to share a limited amount of resources among different companies that might be facing financial difficulties. The objective is to minimize the total long term cost incurred by the economy due to default events. Using the framework of multiarmed restless bandits and, assuming a two-state evolution of the default risk, the optimal dynamic resource sharing policy is determined. This policy assigns an index value to each company, which orders its priority to be funded. We obtain an analytical expression for this index, which generalizes the return-on-investment (ROI) index under the static setting, and we analyse the influence of the future events on the optimal dynamic policy. A discussion about the structure of the optimal dynamic policy is provided, as well as some extensions of the model.