The Rural School from Within. M. G. Kirkpatrick

The Sherrington-Kirkpatrick model

The Sherrington-Kirkpatrick (SK) model was introduced by David Sherrington and Scott Kirkpatrick in 1975 as a simple ‘solvable’ (in their words) model for spin-glasses. Spin-glasses are some type of magnetic alloys, and ‘solvable’ meant that the asymptotic free entropy density could be computed exactly. It turns out that the original SK solution was incorrect and in fact inconsistent (the autho...

The M/G/1+G queue revisited

We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also briefly treat the analogous...

From M/G/1 and M/G/infinity to Simulation: Staged Service Performance Design

There are various techniques for dealing with server saturation. Under duress, some variation of admission control is usually applied, including possibly refusing (aka “throttling”) all arrivals. As parallelism, threading, etc. become commonplace, alternative approaches to servicing heavy workloads are feasible. For a given stream of arriving requests, classical M/G/1 and M/G/infinity queuing m...

Conditional inter-departure times from the M/G/s queue

We study the mean and the distribution of the time elapsing between two consecutive departures from the stationary M/G/s queue given the number of customers left behind by the first departure is equal to n. It is conjectured that if the failure rate of the service time distribution is increasing (decreasing), then (i) the limit of the mean conditional inter-departure time as n tends to infinity...

Nonparametric inference from the M/G/1 workload