Estimating Service Times in Batch-Sharing Queues

• Activity Number: 188
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Xuan Che*+ and Chunxiao Zhou and Ao Yuan and Minh Hyunh
• Companies: NIH and NIH and Georgetown University and NIH
• Keywords: measurement error ; generalized linear mixed model ; queueing model ; nonparametric

Abstract

In a queueing model it is of interest to know how much time a task is spent idle or being serviced. A single server in a queue may handle multiple tasks simultaneously while allowing flexible service policies. We develop a batch sharing queues, generated by task scheduling and reporting patterns. We categorize each task into one of p classes, and assume no task is serviced across multiple batches. The service time for each task in class P is assumed to be generated from the same distribution, and we try to estimate the first and second moment of the service time of each class. Two types of measurement errors may occur in this model: the error associated with the imperfect observation of total batch time, and the error of violation of single batch processing assumption. We develop linear mixed measurement error models (LMMeM) to describe these variations, investigate the identifiability of these systems, introduce total least square and random coefficient estimates for the service times, and explore the consistency of the estimates. We demonstrate our methods using simulated data and claimant queues of Social Security Administration disability determination hearing offices.