Although the application of new, reduced aircraft separation minima can directly increase runway throughput, the impact thereof on the traffic flow of aircraft arriving at the destination airport has not been discussed yet. This paper proposes a data-driven and queue-based modeling approach and presents an analysis of the impact on the delay time of arriving aircraft in the airspace within a radius of 100 nautical miles around an airport. The parameters of our queuing model were estimated by analysing the data contained in the radar tracks and flight plans for flights that arrived at Tokyo International Airport during the 2 years of 2016 and 2017. The results clarified the best arrival strategy according to the distance from the arrival airport: The combination of airspace capacity control and reduction of the flight time and separation variance is the most powerful solution to mitigate delays experienced by arriving traffic while also allowing an increase in the amount of arrival traffic. The application of new wake vortex categories would enable us to increase the arrival traffic to 120%. In addition, the arrival delay time could be minimised by implementing the proposed arrival traffic strategies together with automation support for air traffic controllers.

In this paper, we use queuing theory to model the number of insured households in an insurance portfolio. The model is based on an idea from Boucher and Couture-Piché (2015), who use a queuing theory model to estimate the number of insured cars on an insurance contract. Similarly, the proposed model includes households already insured, but the modeling approach is modified to include new households that could be added to the portfolio. For each household, we also use the queuing theory model to estimate the number of insured cars. We analyze an insurance portfolio from a Canadian insurance company to support this discussion. Statistical inference techniques serve to estimate each parameter of the model, even in cases where some explanatory variables are included in each of these parameters. We show that the proposed model offers a reasonable approximation of what is observed, but we also highlight the situations where the model should be improved. By assuming that the insurance company makes a $1 profit for each one-year car exposure, the proposed approach allows us to determine a global value of the insurance portfolio of an insurer based on the customer equity concept.

A mathematical model based on queuing theory is used to study the dynamics of environmental influence on twin pairs. The model takes into consideration genetic factors and effects of non-shared environment. Histograms are exploited as base analysed characteristics, with the method of minimum chi-square yielding estimated characteristics. The proposed technique was applied to analysis of longitudinal data for MZ and DZ twins. It was shown that the same environment impact may yield different contributions to final variances of the IQ parameters under investigation. Magnitudes of these contributions depend on the genetic factor represented by distributions of an analysed parameter at the point of birth. Twin Research (2000) 3, 92–98.

A neural model with N interacting neurons is considered. A firing of neuron i delays the firing times of all other neurons by the same random variable θ(i), and in isolation the firings of the neuron occur according to a renewal process with generic interarrival time Y(i). The stationary distribution of the N-vector of inhibitions at a firing time is computed, and involves waiting distributions of GI/G/1 queues and ladder height renewal processes. Further, the distribution of the period of activity of a neuron is studied for the symmetric case where θ(i) and Y(i) do not depend upon i. The tools are probabilistic and involve path decompositions, Palm theory and random walks.

Sharp upper and lower reliability bounds for the ℒ- and -classes of life distributions with a given mean are provided. Bounds are also given for a distribution which is related to a known distribution (not necessarily exponential) through the Laplace order.

The behavior of queuing systems with two servers and one waiting room is investigated. It is shown that if the service time is constant, then the difference between the times to service completion of the two servers (phase difference) tends to a constant, for increasing input intensities. This phenomenon holds for a wide class of arrival processes, but not when the service time has even a small variability. These results imply that the delay is not stochastically monotone in the input intensity. In general, we conjecture that the behavior of the phase differences, and delays, depends on whether the size of the waiting room is even or odd.

A simple birth-death model of particle fluctuations is studied where at each discrete time a birth and/or death may occur. We show that if the probability of a birth does not depend on the number of particles present and if births and deaths are independent, then the times between successive deaths are independent geometrically distributed random variables, which is false in the general case. Since the above properties of the times between successive neuron firings have been observed in nerve cells, the model proposed in [2] obtains added credence.

Using some well-known and some recently proved asymptotic properties of regenerative processes, we present a new proof in a general regenerative setting of the equivalence of the limiting distributions of a stochastic process at an arbitrary point in time and at the time of an event from an associated Poisson process. From the same asymptotic properties, several conservation equations are derived that hold for a wide class of GI/G/1 priority queues. Finally, focussing our attention on the alternating-priority queue with Poisson arrivals, we use both types of result to give a new, simple derivation of the expected steady-state delay in the queue in each class.

This paper discusses the response process when a Poisson process interacts with a renewal process in such a way that one or more points of the Poisson process eliminate a random number of consecutive points of the renewal process. A queuing situation is devised such that the c.d.f. of the length of the busy period is the same as the c.d.f. of the length of time intervals of the renewal response process. The Laplace-Stieltjes transform is obtained and from this the expectation of the time intervals of the response process is derived. For a special case necessary and sufficient conditions for the response process to be a Poisson process are found.