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A queuing model is presented in which delay stems from a disparity between the order at which service is provided to customers and the order at which they may leave the system. Consider, for example, wives waiting in cars-single file-for the arrival of their husbands by a common train. A car is ready to leave when its passenger takes his seat but may have to wait for the departure of all cars preceding it in the lane. Initially, the probability function of waiting is determined for a single, finite queue. Next, the consequences of splitting the single queue into several parallel queues with identical discipline are explored. The results of the analysis are applied to a parking lot design problem. [ABSTRACT FROM AUTHOR]

In a recent paper a traffic assignment model has been constructed in which the cost on a link may depend not only on its load, but also on the loads on other links of the network. In this paper it is shown that this model is also capable of handling the case of several classes of users in the same transportation network each of which has an individual cost function and, at the same time, contributes to its own and other classes' cost functions in an individual way. Typical applications arise not only in street networks where vehicles of different types share the same roads (e.g., trucks and passenger cars) but also in other types of transportation networks (e.g., telephone networks). An algorithm is constructed for finding the system-optimizing flow pattern for such a multiclass-user transportation network. [ABSTRACT FROM AUTHOR]

A model is developed for the flow of automobiles in one direction along a two-lane, country road. The model takes into account the fact that cars differ in speed, that slower cars accumulate queues behind them, and that the rate of escape from such a queue, by passing the lead car, depends on the speed of the lead car, on the nature of the road, and on the density of traffic going in the opposite direction. Equations for the stochastic steady state of the system reduce to an in- integral equation for the mean queue length, as a function of lead- car speed and of a queue-delay parameter. Solutions are obtained, with tables and graphs, for two different assumptions regarding the dependence of passing delay on lead-car speed. In both cases the model exhibits a sudden change from sparse-traffic conditions, where queuing is rare and delay of the faster cars is minimal, to the dense-traffic conditions where nearly all cars find themselves trapped in a slow queue, as the passing-delay parameter is increased beyond its transitional value. Such a sudden `phase-change' in traffic character is typical of actual traffic under the specified conditions. Measured dependence of queue length on lead-car speed checks nicely with the model, for sparse-traffic conditions. [ABSTRACT FROM AUTHOR]

Starting with a basic model of volley fire against a group of homogeneous passive targets, a series of discrete approximations to the expected number of surviving targets is proposed. Some of these yield quite good approximations over a reasonably wide range of parameter values. Continuous analogues of these approximations are described, and it is shown how various Lanchester-type equations arise in a natural way from these continuous analogues. [ABSTRACT FROM AUTHOR]

This paper considers a modification of the single-car intersection delay problem in which the waiting driver, upon finding a suitable gap for crossing also examines the succeeding one, and uses it if it is larger. It is shown that the additional delay time caused by this method of gap acceptance is generally quite small. [ABSTRACT FROM AUTHOR]

The linear theory of single-lane traffic flow is generalized by using an integral transform technique well-known in other branches of applied science. This technique introduces the idea of a memory function that describes the way in which a driver processes the information he receives from a lead vehicle. Several analytical examples are computed and the earlier linear model is discussed as a special case of the more general theory. [ABSTRACT FROM AUTHOR]

This paper presents a study of several aspects of the theory of car queues. In it we consider a situation in which there is traffic on a main highway and a queue of cars on a side road waiting to merge. First we consider a case in which the lead driver chooses to merge on the basis of whether the gap in main highway traffic exceeds a service time that is chosen from a probability density. An expression for the generating function of the steady-state distribution and the waiting-time distribution are derived. Secondly, the critical input to the side road is determined such that for all larger inputs the queue is transient. In particular we consider the effect of the move up time (of the second car in a queue) on this parameter. Finally, we present the results of a study by simulation techniques for the analysis of traffic queuing models. A discussion of the use of importance sampling in improving simulation studies is given, and a comparison made between theoretical and simulation results. [ABSTRACT FROM AUTHOR]

The response delay in clearing the queue of automobiles waiting at a traffic light can be modeled by allowing one car to leave at the end of each of a series of discrete intervals in time. The steady-state queue formed at a cycle traffic light is discussed for general stationary arrival processes. A method of solution for the case where arrivals are Poisson is described. General formulas are given for the probability of not clearing the queue during a cycle and for the expected wait at the light. [ABSTRACT FROM AUTHOR]

A vehicle waiting at an intersection with a major road makes a merging maneuver into the mainstream traffic, thus possibly requiring oncoming traffic to slow down. This paper examines the resulting disturbance that this forced entry may create in the main stream, assumed to be a renewal process. After showing that the disturbance propagation is formally equivalent to the busy period of a related queuing model, explicit results on the length of disturbance period and the number of vehicles affected are obtained for the case of Poisson traffic. It is shown that there is some minimal main-stream headway which should be forced in order to maximize the rate at which entries can be made from the secondary road. Finally, two measures of accident potential for the merging maneuver are discussed. [ABSTRACT FROM AUTHOR]

We consider here the delays suffered by a car in passing through a long sequence of synchronized traffic signals, assuming that the density of traffic is low enough that one can neglect the interactions between cars, and that each car has a desired speed which it maintains at all times except when stopped by a traffic light By considering the special case of equally spaced lights, we conclude that for short distances between lights the relative phase of the traffic lights that gives a minimum average delay per light depends upon the fraction of green time of the traffic cycle For long distances between lights, it is found that the usual progressive timing of lights may cause greater delays than a random synchronization but in such cases there are other schemes of synchronization that are still better Finally, some qualitative effects of velocity fluctuations are discussed [ABSTRACT FROM AUTHOR]

The operating speed y of a car is a function of desired speed x and traffic density λ, where x and y are random variables, and λ a real parameter. Relationships are proposed between the distributions of x and y and quantities which occur in empirical studies of traffic. It is postulated that for large λ queuing theory may be usefully employed, and several necessary modifications are discussed A résumé of literature is included. [ABSTRACT FROM AUTHOR]

In a Markovian decision problem, choice of an action determines an immediate return and the probability of moving to the next state. It is desired to maximize the expected total of discounted future returns. If upper and lower bounds on the optimal expected return are available, a simple test is described that may show that certain actions are suboptimal, permanently eliminating them from further consideration. This test may be incorporated into the dynamic programming routine for solving the decision problem. This was tried on Howard's automobile replacement problem, using the upper and lower bounds described in "A Modified Dynamic Programming Method" (J. Math. Anal. and Appl. 14, April, 1966). The amount of computation required by the dynamic programming routine was reduced, conservatively, by 75 per cent. [ABSTRACT FROM AUTHOR]