We consider the following Markovian dynamic on point processes: at constant rate and with
equal probability, either the rightmost atom of the current configuration is removed, or a new …

Distributed load balancing is the act of allocating jobs among a set of servers as evenly as
possible. The static interpretation of distributed load balancing leads to formulating the load …

Vladas was born in Vilnius, Lithuania, on August 23, 1963, and did his undergraduate
studies in Mathematics from 1982 to 1985 at Vilnius University. There, in 1986, he received …

We consider a single‐server system with service stations in each point of the circle.
Customers arrive after exponential times at uniformly distributed locations. The server moves …

Fix integers d≥ 2 and k≥ d− 1. Consider a random walk X 0, X 1,… in R d in which, given X
0, X 1,…, X n (n≥ k), the next step X n+ 1 is uniformly distributed on the unit ball centred at X …

Each site of Z hosts a queue with arrival rate λ. A single server, starting at the origin, serves
its current queue at rate μ until that queue is empty, and then moves to the longest …

We consider a greedy walk on a Poisson process on the real line. It is known that the walk
does not visit all points of the process. In this paper we first obtain some useful …

We study a queueing system with Poisson arrivals on a bus line indexed by integers. The
buses move at constant speed to the right, and the time of service per customer getting on …

We study a queueing system with Poisson arrivals on a bus line indexed by integers. The
buses move at constant speed to the right and the time of service per customer getting on …

The greedy walk is a walk on a point process that always moves from its current position to
the nearest not yet visited point. We consider here various point processes on two lines. We …