Queues with updating information: finding the amplitude of oscillations. (English) Zbl 1494.34182
Summary: 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 \(\Delta\). 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 \(\Delta\) is large. Our analysis provides new insight for systems that use updates as a way of disseminating information to customers.
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 34K21 | Stationary solutions of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K18 | Bifurcation theory of functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
| 90B22 | Queues and service in operations research |
| 34K07 | Theoretical approximation of solutions to functional-differential equations |
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