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Unlimited access to a motorway network can, in overloaded conditions, cause a loss of throughput. Ramp metering, by controlling access to the motorway at onramps, can help avoid this loss of throughput. The queues that form at onramps are dependent on the metering rates chosen at the onramps, and these choices affect how the capacities of different motorway sections are shared amongst competing flows. In this paper we perform an analytical study of a fluid, or differential equation, model of a linear network topology with onramp queues. The model allows for adaptive arrivals, in the sense that the rate at which external traffic enters the queue at an onramp can depend on the current perceived delay in that queue. The model also includes a ramp metering policy which uses global onramp queue length information to determine the rate at which traffic enters the motorway from each onramp. This ramp metering policy minimizes the maximum delay over all onramps and produces equal delay times over many onramps. The paper characterizes both the dynamics and the equilibrium behavior of the system under this policy. While we consider an idealized model that leaves out many practical details, an aim of the paper is to develop analytical methods that yield interesting qualitative insights and might be adapted to more general contexts. The paper can be considered as a step in developing an analytical approach towards studying more complex network topologies and incorporating other model features. [ABSTRACT FROM AUTHOR]

It is easy to see that I f i ( I k i ) is of order HT ht if HT ht 's are light-tailed. Assume that HT ht new jobs arrive at the beginning of time slot I k i , and HT ht is an i.i.d. sequence. Denote by HT ht and let I f i ( I k i ) be such that HT ht for HT ht . [Extracted from the article]

The article presents a study on the performance of the accumulating priority queue, also known as the time-dependent priority queue as developed by L. Kleinrock in his study of queueing systems. Topics include waiting time distributions for priority queues, the accumulation of priority as a linear function of time, the mathematical aspects of the maximum priority process, and non-preemptive priority.

We study a simple network with two parallel batch-service queues, where service at a queue commences when the batch is full and each queue is served by infinitely many servers. A stream of general arrivals observe the current state of the system on arrival and choose which queue to join to minimize their own expected transit time. We show that for each set of parameter values there exists a unique user equilibrium policy and that it possesses various monotonicity properties. User equilibrium policies for probabilistic routing are also discussed and compared with the state-dependent setting. [ABSTRACT FROM AUTHOR]

Consider a system of two queues in parallel, one of which is a ⋅| M|1 single-server infinite capacity queue, and the other a ⋅| G|∞ batch service queue. A stream of general arrivals choose which queue to join, after observing the current state of the system, and so as to minimize their own expected delay. We show that a unique user equilibrium (user optimal policy) exists and that it possesses various monotonicity properties, using sample path and coupling arguments. This is a very simplified model of a transportation network with a choice of private and public modes of transport. Under probabilistic routing (which is equivalent to the assumption that users have knowledge only of the mean delays on routes), the network may exhibit the Downs-Thomson paradox observed in transportation networks with expected delay increasing as the capacity of the ⋅| M|1 queue (private transport) is increased. We give examples where state-dependent routing mitigates the Downs-Thomson effect observed under probabilistic routing, and providing additional information on the state of the system to users reduces delay considerably. [ABSTRACT FROM AUTHOR]

We consider admission and routing controls for a system of N parallel tandem queues with finite buffers as N becomes large, with the aim of minimizing costs due to loss. We obtain the fluid limit as N→∞, and solve a related optimization problem. Asymptotically, for N large, the optimal cost and associated control take one of two forms, depending on the ratio between the cost of blocking an arrival at entry and discarding after service at the first queue. [ABSTRACT FROM AUTHOR]