63 citations · 189 across the 26 of their papers we have counts for
5 papers · 1 filter
Learning random points from geometric graphs or orderings
Josep Diaz, Colin McDiarmid, Dieter Mitsche
Suppose that there is a family of random points for , independently and uniformly distributed in the square of area .…
Balanced routing of random calls
Malwina J. Luczak, Colin McDiarmid
We consider an online network routing problem in continuous time, where calls have Poisson arrivals and exponential durations. The first-fit dynamic alternative routing algorithm s…
Asymptotic distributions and chaos for the supermarket model
Malwina J. Luczak, Colin McDiarmid
In the supermarket model there are n queues, each with a unit rate server. Customers arrive in a Poisson process at rate λn, where 0<λ<1. Each customer chooses d > 2 queues uniform…
On the maximum queue length in the supermarket model
Malwina J. Luczak, Colin McDiarmid
There are queues, each with a single server. Customers arrive in a Poisson process at rate , where . Upon arrival each customer selects servers uniformly at…
On the power of two choices: Balls and bins in continuous time
Malwina J. Luczak, Colin McDiarmid
Suppose that there are n bins, and balls arrive in a Poisson process at rate λn, where λ>0 is a constant. Upon arrival, each ball chooses a fixed number d of random bins, and is pl…