Marginal productivity index policies for problems of admission control and routing to parallel queues with delay

In this paper we consider the problem of admission control of Bernoulli arrivals to a buffer with geometric server, in which the controller’s actions take effect one period after the actual change in the queue length. An optimal policy in terms of marginal productivity indices (MPI) is derived for this problem under the following three performance objectives: (i) minimization of the expected total discounted sum of holding costs and rejection costs, (ii) minimization of the expected time-average sum of holding costs and rejection costs, and (iii) maximization of the expected time-average number of job completions. Our employment of existing theoretical and algorithmic results on restless bandit indexation together with some new results yields a fast algorithm that computes the MPI for a queue with a buffer size of I performing only O(I) arithmetic operations. Such MPI values can be used both to immediately obtain the optimal thresholds for the admission control problem, and to design an index policy for the routing problem (with possible admission control) in the multi-queue system. Thus, this paper further addresses the problem of designing and computing a tractable heuristic policy for dynamic job admission control and/or routing in a discrete time Markovian model of parallel loss queues with one-period delayed state observation and/or action implementation, which comes close to optimizing an infinite-horizon problem under the above three objectives. Our approach seems to be tractable also for the analogous problems with larger delays and, more generally, for arbitrary restless bandits with delays

Study of a Dynamic Cooperative Trading Queue Routing Control Scheme for Freeways and Facilities with Parallel Queues

This article explores the coalitional stability of a new cooperative control policy for freeways and parallel queuing facilities with multiple servers. Based on predicted future delays per queue or lane, a VOT-heterogeneous population of agents can agree to switch lanes or queues and transfer payments to each other in order to minimize the total cost of the incoming platoon. The strategic interaction is captured by an n-level Stackelberg model with coalitions, while the cooperative structure is formulated as a partition function game (PFG). The stability concept explored is the strong-core for PFGs which we found appropiate given the nature of the problem. This concept ensures that the efficient allocation is individually rational and coalitionally stable. We analyze this control mechanism for two settings: a static vertical queue and a dynamic horizontal queue. For the former, we first characterize the properties of the underlying cooperative game. Our simulation results suggest that the setting is always strong-core stable. For the latter, we propose a new relaxation program for the strong-core concept. Our simulation results on a freeway bottleneck with constant outflow using Newell's car-following model show the imputations to be generally strong-core stable and the coalitional instabilities to remain small with regard to users' costs.Comment: 3 figures. Presented at Annual Meeting Transportation Research Board 2018, Washington DC. Proof of conjecture 1 pendin

Virtual lines, a deadlock free and real-time routing mechanism for ATM networks

In this paper we present a routing mechanism and buffer allocation mechanism for an ATM switching fabric. Since the fabric will be used to transfer multimedia traffic it should provide a guaranteed throughput and a bounded latency. We focus on the design of a suitable routing mechanism that is capable to fulfil these requirements and is free of deadlocks. We will describe two basic concepts that can be used to implement deadlock free routing. Routing of messages is closely related to buffering. We have organized the buffers into parallel fifos, each representing a virtual line. In this way we not only have solved the problem of Head Of Line blocking, but we can also give real-time guarantees. We will show that for local high-speed networks it is more advantageous to have a proper flow control than to have large buffers. Although the virtual line concept can have a low buffer utilization, the transfer efficiency can be higher. The virtual lines concept allows adaptive routing. The total throughput of the network can be improved by using alternative routes. Adaptive routing is attractive in networks where alternative routes are not much longer than the initial route(s). The network of the switching fabric is built up from switching elements interconnected in a Kautz topology