Queues with Updating Information: Finding the Amplitude of Oscillations

Abstract

Many service systems provide customers with information about the system so that customers can make an informed decision about whether to join or not. Many of these systems provide information in the form of an update. Thus, the information about the system is updated periodically in increments of size [Formula: see text]. It is known that these updates can cause oscillations in the resulting dynamics. However, it is an open problem to explicitly characterize the size of these oscillations when they occur. In this paper, we solve this open problem and show how to exactly calculate the amplitude of these oscillations via a fixed point equation. We also calculate closed form approximations via Taylor expansions of the fixed point equation and show that these approximations are very accurate, especially when [Formula: see text] is large. Our analysis provides new insight for systems that use updates as a way of disseminating information to customers.

Queues with Delayed Information: Analyzing the Impact of the Choice Model Function

“…In an age where information is readily available, it is an important problem to understand how information affects the decision making of customers who want to join queueing systems. In some applications, such as amusement parks, transportation systems, and even telecommunication systems, it has been observed that the information given to the customers can potentially be delayed Doldo and Pender [5], Novitzky and Pender [14], Pender et al [19,18], Nirenberg et al [12]. This delay in information can be caused by factors such as the fact that it can take time to process and send information about queue lengths to the customers and thus the information that customers actually receive describes the queue lengths from some amount of time in the past.…”

“…Some of the literature has examined queueing systems where the delay is not constant. For example, a queueing model that uses delayed updating information is examined in Doldo and Pender [5], Novitzky and Pender [14]. Additionally, queueing models with distributed delays have been studied by considering distributed delay equation models in Doldo and Pender [2], Novitzky and Pender [13], though it is worth noting that distributed delay models exhibit different dynamics in general than simply replacing the constant delay with a random variable in standard models, as discussed in Doldo and Pender [4].…”