On Queues with Poisson Arrivals

Synchronized queues with deterministic arrivals

We consider m independent exponential servers in parallel, driven by the same deterministic input. This is a modification of the Flatto-Hahn-Wright model which turns out to be easily tractable. We focus on the time-stationary distribution of the number of customers which is obtained using the Palm inversion formula.

Poisson and Gaussian Approximations for Multi-Server Queues with Batch Arrivals and Batch Abandonment

In this paper, we consider nonstationary multi-server queues and multiserver loss queues with batch arrivals and where we allow customer abandonment to also occur as a Markovian batch process. To estimate the performance of the system, we develop two new approximations that take advantage of the functional Kolmogorov forward equations. The first approximation we develop uses the Poisson distrib...

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server’s movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The se...

A Approximations in Finite Capacity /? Multi-server Queues with Poisson Arrivals

In (his paper^-we^consider;an M/G/k queuelng model having finite capacity N . That Is, a model In which customers, arriving In accordance with a Polsson process having rate ■h > , enter the system If there are less than N others present when they arrive, and are then serviced by one of k servers, each of whom has service distribution G . Upon entering, a customer will either Immediately enter s...

Monotonicity Results for Queues with Doubly Stochastic Poisson Arrivals: Ross's Conjecture