Related papers: On The Waiting Time for A M/M/1 Queue with Impatie…
We investigate the response function of human agents as demonstrated by written correspondence, uncovering a new universal pattern for how the reactive dynamics of individuals is distributed across the set of each agent's contacts. In…
This paper re-examines the use of response time to infer problem complexity. It revisits a canonical Wald model of optimal stopping, taking signal-to-noise ratio as a measure of problem complexity. While choice quality is monotone in…
We consider polling models in the sense of Takagi (MIT Press, 1986). In our case, the feature of the server is that it may be forced to wait idly for new messages at an empty queue instead of switching to the next station. We propose four…
A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the…
We study properties of basic solutions in systems with dime delays and $S^1$-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the…
In the literature, retrial queues with batch arrivals and heavy service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The…
Arrival times of requests to print in a student laboratory were analyzed. Inter-arrival times between subsequent requests follow a universal scaling law relating time intervals and the size of the request, indicating a scale invariant…
Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be…
Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…
We provide upper and lower bounds for the expected length $\mathbb E(L_{n,m})$ of the longest common pattern contained in $m$ random permutations of length $n$. We also address the tightness of the concentration of $L_{n,m}$ around $\mathbb…
Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern $q$ in permutations that avoid another given pattern $r$. In some cases, we find the pattern that occurs least often, (resp. most…
This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. Specifically, every…
In this paper, we study stability and latency of routing in wireless networks where it is assumed that no collision will occur. Our approach is inspired by the adversarial queuing theory, which is amended in order to model wireless…
Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the waiting time for the first completed…
Mean field models are a popular tool used to analyse load balancing policies. In some cases the waiting time distribution of the mean field limit has an explicit form. In other cases it can be computed as the solution of a set of…
A family of wave packets with power law tails are employed to analyze the long time dependence of the corresponding probability density. The densities, associated to packets for free particles in the one-dimensional space, with sufficiently…
The goal of developing a firmer theoretical understanding of inhomogenous temporal processes -- in particular, the waiting times in some collective dynamical system -- is attracting significant interest among physicists. Quantifying the…
Waiting time is an important transport quantity that is complementary to average current and its fluctuation. So far all the studies of waiting time distribution (WTD) are limited to steady state transport (either dc or ac). In this work,…
Many wireless protocols wait a small and random amount of time which is called jitter before sending a packet to avoid high contention and packet collision. Jitter has been already proposed for many routing protocols including AODV and…
Cognitive radio transceiver can opportunistically access the underutilized spectrum resource of primary systems for new wireless services. With interleave implementation, the secondary transmission may be interrupted by the primary user's…