Three Dimensional Hydrodynamic Modeling Study, Craney Island eastward expansion, lower James River and Elizabeth River, Virginia

The Craney Island Eastward Expansion Hydrodynamic Model Study was conducted in three phases: 1) model calibration and verification for the Elizabeth River, 2) model testing of four Craney Island expansion options using single variable runs (using a single variable, tidal range, for model input), 3) model testing of two expansion options using historical runs (using multiple variables in real time for model input). The expansion option designs were evaluated for both global and local hydrodynamic change through simulation comparisons with the Base Case condition

Performance analysis of polling systems with retrials and glue periods

We consider gated polling systems with two special features: (i) retrials, and (ii) glue or reservation periods. When a type-$i$ customer arrives, or retries, during a glue period of station $i$, it will be served in the next visit period of the server to that station. Customers arriving at station $i$ in any other period join the orbit of that station and retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. For the case of exponentially distributed glue periods, we present an algorithm to obtain the moments of the number of customers in each station. For generally distributed glue periods, we consider the distribution of the total workload in the system, using it to derive a pseudo conservation law which in its turn is used to obtain accurate approximations of the individual mean waiting times. We also consider the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times

Critically loaded k-limited polling systems

We consider a two-queue polling model with switch-over times and k-limited service (serve at most ki customers during one visit period to queue i) in each queue. The major benefit of the k-limited service discipline is that it - besides bounding the cycle time - effectuates prioritization by assigning different service limits to different queues. System performance is studied in the heavy-traffic regime, in which one of the queues becomes critically loaded with the other queue remaining stable. By using a singular-perturbation technique, we rigorously prove heavy-traffic limits for the joint queue-length distribution. Moreover, it is observed that an interchange exists among the first two moments in service and switch-over times such that the HT limits remain unchanged. Not only do the rigorously proven results readily carry over to N( ≥ 2) queue polling systems, but one can also easily relax the distributional assumptions. The results and insights of this note prove their worth in the performance analysis of Wireless Personal Area Networks (WPAN) and mobile networks, where different users compete for access to the shared scarce resources

Networks of fixed-cycle intersections

\u3cp\u3eWe present an algorithmic method for analyzing networks of intersections with static signaling, with as primary example a line network that allows traffic flow over several intersections in one main direction. The method decomposes the network into separate intersections and treats each intersection in isolation using an extension of the fixed-cycle traffic-light (FCTL) queue. The network effects are modeled by matching the output process of one intersection with the input process of the next (downstream) intersection. This network analysis provides insight into wave phenomena due to vehicles experiencing progressive cascades of green lights and sheds light on platoon forming in case of imperfections. Our algorithm is shown to match results from extensive discrete-event simulations and can also be applied to more complex network structures.\u3c/p\u3

Networks of fixed-cycle intersections

We present an algorithmic method for analyzing networks of intersections with static signaling, with as primary example a line network that allows traffic flow over several intersections in one main direction. The method decomposes the network into separate intersections and treats each intersection in isolation using an extension of the fixed-cycle traffic-light (FCTL) queue. The network effects are modeled by matching the output process of one intersection with the input process of the next (downstream) intersection. This network analysis provides insight into wave phenomena due to vehicles experiencing progressive cascades of green lights and sheds light on platoon forming in case of imperfections. Our algorithm is shown to match results from extensive discrete-event simulations and can also be applied to more complex network structures

Generalized gap acceptance models for unsignalized intersections

This paper contributes to the modeling and analysis of unsignalized intersections. In classical gap acceptance models vehicles on the minor road accept any gap greater than the CRITICAL gap, and reject gaps below this threshold, where the gap is the time between two subsequent vehicles on the major road. The main contribution of this paper is to develop a series of generalizations of existing models, thus increasing the model's practical applicability significantly. First, we incorporate {driver impatience behavior} while allowing for a realistic merging behavior; we do so by distinguishing between the critical gap and the merging time, thus allowing MULTIPLE vehicles to use a sufficiently large gap. Incorporating this feature is particularly challenging in models with driver impatience. Secondly, we allow for multiple classes of gap acceptance behavior, enabling us to distinguish between different driver types and/or different vehicle types. Thirdly, we use the novel M$^X$/SM2/1 queueing model, which has batch arrivals, dependent service times, and a different service-time distribution for vehicles arriving in an empty queue on the minor road (where `service time' refers to the time required to find a sufficiently large gap). This setup facilitates the analysis of the service-time distribution of an arbitrary vehicle on the minor road and of the queue length on the minor road. In particular, we can compute the MEAN service time, thus enabling the evaluation of the capacity for the minor road vehicles

Generalized gap acceptance models for unsignalized intersections

\u3cp\u3e This paper contributes to the modeling and analysis of unsignalized intersections. In classical gap acceptance models vehicles on the minor road accept any gap greater than the critical gap, and reject gaps below this threshold, where the gap is the time between two subsequent vehicles on the major road. The main contribution of this paper is to develop a series of generalizations of existing models, thus increasing the model’s practical applicability significantly. First, we incorporate driver impatience behavior while allowing for a realistic merging behavior; we do so by distinguishing between the critical gap and the merging time, thus allowing multiple vehicles to use a sufficiently large gap. Incorporating this feature is particularly challenging in models with driver impatience. Secondly, we allow for multiple classes of gap acceptance behavior, enabling us to distinguish between different driver types and/or different vehicle types. Thirdly, we use the novel M \u3csup\u3eX\u3c/sup\u3e /SM2/1 queueing model, which has batch arrivals, dependent service times, and a different service-time distribution for vehicles arriving in an empty queue on the minor road (where ‘service time’ refers to the time required to find a sufficiently large gap). This setup facilitates the analysis of the service-time distribution of an arbitrary vehicle on the minor road and of the queue length on the minor road. In particular, we can compute the mean service time, thus enabling the evaluation of the capacity for the minor road vehicles. \u3c/p\u3

Visualizing multiple quantile plots

Multiple quantile plots provide a powerful graphical method for comparing the distributions of two or more populations. This paper develops a method of visualizing triple quantile plots and their associated con¿dence tubes, thus extending the notion of a QQ plot to three dimensions. More speci¿cally, we consider three independent one-dimensional random samples with corresponding quantile functions Q1, Q2 and Q3, respectively. The triple quantile (QQQ) plot is then de¿ned as the three-dimensional curve Q.(p) = (Q1.(p), Q2.(p), Q3.(p)), where 0 <p <1. The empirical likelihood method is used to derive simultaneous distribution-free con¿dence tubes for Q. We apply our method to an economic case study of strike durations, and to an epidemiological study involving the comparison of cholesterol levels among three populations. These data as well as the Mathematica code for computation of the tubes are available online