Related papers: Waiting-time paradox in 1922
Suppose that you're going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer - possibly much longer - than what the bus schedule suggests intuitively. This phenomenon,…
Bus bunching is a perennial phenomenon that not only diminishes the efficiency of a bus system, but also prevents transit authorities from keeping buses on schedule. We present a physical theory of buses serving a loop of bus stops as a…
The remaining travel time of a plane shortens with every minute that passes from its departure, and a flame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun…
We study the Braess paradox in the transport network as originally proposed by Braess with totally asymmetric exclusion processes (TASEPs) on the edges. The Braess paradox describes the counterintuitive situation in which adding an edge to…
Despite being a major component in the teaching of special relativity, the twin `paradox' is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often…
Bus bunching is a curse of transportation systems such as buses in a loop. Here we present an analytical method to find the number of revolutions before two buses bunch in an idealised system, as a function of the initial distance and the…
The clock paradox is analyzed for the case when the onward and return trips cover the same <<distance>> (as observed by the traveling twin) but at unequal velocities. In this case the stationary twin observes the distances covered by her…
The Classical Twin Paradox is widely dealt in literature and neatly resolved. In addition, it is also well known that, when looking at two systems which are boosted relative to each other, the concept of the simultaneous effect of a quantum…
This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space…
Bus bunching is ostensibly regarded as a detrimental phenomenon in bus systems. We study a bus loop with two bus stops, one regular and one spike bus stop, where bunched buses can outperform staggered buses. The spike bus stop models a bus…
The Braess paradox describes the counterintuitive situation that the addition of new roads to road networks can lead to higher travel times for all network users. Recently we could show that user optima leading to the paradox exist in…
The classical network configuration introduced by Braess in 1968 is of fundamental significance because Valiant and Roughgarden showed in 2006 that `the "global" behaviour of an equilibrium flow in a large random network is similar to that…
This paper proposes a macroscopic model to describe the equilibrium distribution of passenger arrivals for the morning commute problem in a congested urban rail transit system. We use a macroscopic train operation sub-model developed by Seo…
This mathematical recreation extends the analysis of a recent paper, asking when a traveller at a bus stop and not knowing the time of the next bus is best advised to wait or to start walking toward the destination. A detailed analysis and…
We discuss the twin paradox or the clock paradox under the small velocity approximation of special relativity. In this paper the traveller twin of the standard twin parable sets out with a non-relativistic speed for the trip leaving behind…
The paradoxes of thermodynamics and statistical physics are unavoidable in the study of physical paradoxes because of their importance at the time they came to be as well as the frequency of their appearance in historical studies of…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
We have introduced excluded volume effect, which is an important factor to model a realistic pedestrian queue, into queueing theory. The probability distributions of pedestrian number and pedestrian waiting time in a queue have been…
One of the most discussed peculiarities of Einstein's theory of relativity is the twin paradox, the fact that the time between two events in space-time appears to depend on the path between these events. We show that this time discrepancy…
We investigate the stochastic transfer synchronization problem, which seeks to synchronize the timetables of different routes in a transit network to reduce transfer waiting times, delay times, and unnecessary in-vehicle times. We present a…