Related papers: Stability of the Greedy Algorithm on the Circle
Each site of $\mathbb{Z}$ hosts a queue with arrival rate $\lambda$. A single server, starting at the origin, serves its current queue at rate $\mu$ until that queue is empty, and then moves to the longest neighbouring queue. In the…
This paper studies a spatial queueing system on a circle, polled at random locations by a myopic server that can only observe customers in a bounded neighborhood. The server operates according to a greedy policy, always serving the nearest…
We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space-time half plane. The server…
Motivated by the use of high speed circuit switches in large scale data centers, we consider the problem of circuit switch scheduling. In this problem we are given demands between pairs of servers and the goal is to schedule at every time…
The algorithmic small-world phenomenon, empirically established by Milgram's letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. However, from today's perspective his model has several severe…
In this paper, we design a greedy routing on networks of mobile agents. In the greedy routing algorithm, every time step a packet in agent $i$ is delivered to the agent $j$ whose distance from the destination is shortest among searched…
Large scale decentralized communication systems have introduced the new trend towards online routing where routing decisions are performed based on a limited and localized knowledge of the network. Geometrical greedy routing has been among…
We consider the online minimum cost matching problem on the line, in which there are $n$ servers and, at each of $n$ time steps, a request arrives and must be irrevocably matched to a server that has not yet been matched to, with the goal…
We consider the problem of forwarding packets arriving online with their destinations in a line network. In each time step, each router can forward one packet along the edge to its right. Each packet that is forwarded arrives at the next…
Given a random variable $N$ with values in ${\mathbb{N}}$, and $N$ i.i.d. positive random variables $\{\mu_k\}$, we consider a queue with renewal arrivals and $N$ exponential servers, where server $k$ serves at rate $\mu_k$, under two work…
Recurrence and ergodic properties are established for a single--server queueing system with variable intensities of arrivals and service. Convergence to stationarity is also interpreted in terms of reliability theory.
We consider a two station cascade system in which waiting or externally arriving customers at station $1$ move to the station $2$ if the queue size of station $1$ including a customer being served is greater than a given threshold level…
We consider a single-server cyclic polling system with three queues where the server follows an adaptive rule: if it finds one of queues empty in a given cycle, it decides not to visit that queue in the next cycle. In the case of limited…
A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…
This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…
By introducing a simple model based on two-dimensional cellular automata, we reveal the relationship between the routing strategies of individual vehicles and the global behavior of transportation networks. Specifically, we characterize the…
We consider a service system model primarily motivated by the problem of efficient assignment of virtual machines to physical host machines in a network cloud, so that the number of occupied hosts is minimized. There are multiple input…
We consider the problem of studying the performance of greedy algorithm on sensor selection problem for stable linear systems with Kalman Filter. Specifically, the objective is to find the system parameters that affects the performance of…
Consider the workload process for a single server queue with deterministic service times in which customers arrive according to a scheduled traffic process. A scheduled arrival sequence is one in which customers are scheduled to arrive at…
We consider a service system model primarily motivated by the problem of efficient assignment of virtual machines to physical host machines in a network cloud, so that the number of occupied hosts is minimized. There are multiple types of…