Please come back later: Benefiting from deferrals in service systems

TL;DR

This paper explores how deferring customers in loss service systems can improve performance, proposing a state-dependent policy for scheduling deferred arrivals and demonstrating its advantages through numerical analysis.

Contribution

It introduces a novel state-dependent deferral policy for loss systems and analyzes its performance benefits compared to simpler policies.

Findings

The proposed policy reduces customer drops compared to naive policies.

Characterization of long-term drop rates under the new policy.

Numerical results show significant performance improvements.

Abstract

The performance evaluation of loss service systems, where customers who cannot be served upon arrival get dropped, has a long history going back to the classical Erlang B model. In this paper, we consider the performance benefits arising from the possibility of deferring customers who cannot be served upon arrival. Specifically, we consider an Erlang B type loss system where the system operator can, subject to certain constraints, ask a customer arriving when all servers are busy, to come back at a specified time in the future. If the system is still fully loaded when the deferred customer returns, she gets dropped for good. For such a system, we ask: How should the system operator determine the rearrival times of the deferred customers based on the state of the system (which includes those customers already deferred and yet to arrive)? How does one quantify the performance benefit of such a deferral policy? Our contributions are as follows. We propose a simple state-dependent policy for determining the rearrival times of deferred customers. For this policy, we characterize the long run fraction of customers dropped. We also analyse a relaxation where the deferral times are bounded in expectation. Via extensive numerical evaluations, we demonstrate the superiority of the proposed state-dependent policies over naive state-independent deferral policies.