Queues with Censored Demand and Autoregressive Net Input

TL;DR

This paper introduces methods to simulate queues with autoregressive net-inputs and estimate censored demand, demonstrated through analyzing U.S. job openings during economic downturns.

Contribution

It presents novel techniques for modeling queues with censored demand and autoregressive inputs, including estimation methods from queue length samples.

Findings

Estimated monthly unsatisfied demand for U.S. nonfarm jobs.

Demonstrated modeling of demand censoring near queue zero.

Applied methods to recession periods.

Abstract

We develop methods for simulating a queue with an autoregressive net-input process and for recovering characteristics of such a net-input process from samples of queue lengths. We apply these methods to the problem of estimating the censored (unsatisfied) demand for the queue's content and show how to model a queue for which the censoring of demand is graduated in a neighborhood of the queue's zero lower bound. As an example, we estimate the monthly unsatisfied demand for U.S. nonfarm jobs based on samples of job openings through a period including the last two recessions.