English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider a model describing the length of two queues that incorporates customer choice behavior based on delayed queue length information. The symmetric case, where the values of the time-delay parameter in each queue are the same, was recently studied. It was shown that under some conditions, the stable equilibrium solution becomes unstable as the common time delay passes a threshold value. This one-time stability switch occurs only at a symmetry-breaking Hopf bifurcation where a family of stable asynchronous limit-cycle solutions arise. In this paper, we examine the non-symmetric case, wherein the values of the time-delay parameter in each queue are different. We show that, in contrast to the symmetric case, the non-symmetric case allows bubbling, multiple stability switches and coexistence of distinct families of stable limit cycles. An investigation of the dynamical behavior of the non-symmetric system in a neighborhood of a double-Hopf bifurcation using numerical continuation explains the occurrence of the bistable limit cycles. Quasi-periodic oscillations were also observed due to the presence of torus bifurcations near the double-Hopf bifurcation. These identifications of the underlying mechanisms that cause unwanted oscillations in the system give a better understanding of the effects of providing delayed information and consequently help in better management of queues.

Bubbling, Bistable Limit Cycles and Quasi-Periodic Oscillations in Queues with Delayed Information