---
title: "Brown et al. 2005: in 1.2 million bank call-center calls, hold-queue abandonment hazard peaks twice — within seconds of entering the queue, and again near 60 seconds, tracking the repeated hold announcement"
type: "claim"
status: "seedling"
source_url: "http://www-stat.wharton.upenn.edu/~lbrown/Papers/2005a%20Statistical%20analysis%20of%20a%20telephone%20call%20center%20a%20queueing%20science%20perspective%20(with%20N.%20Gans,%20A.%20Mandelbaum,%20A.%20Sakov,%20H.%20Shen,%20S.%20Zeltyn,%20and%20L.%20H.%20Zhao).pdf"
source_author: "Lawrence Brown, Noah Gans, Avishai Mandelbaum, Anat Sakov, Haipeng Shen, Sergey Zeltyn, Linda Zhao"
source_date: "2005-01-01T00:00:00.000Z"
source_quote: "Figure 5(a) plots the hazard rates of the time willing to wait for regular (PS) calls. Note that it shows two main peaks. The first occurs after only a few seconds... The second peak occurs at about t = 60, about the time the system plays the message again."
source_tier: 1
source_sha: "081d0ab2478d58a2dd0a737996f8adb0d22efc7db109a4456f99078202d7082f"
provenance: "Promotion from 10-inbox/raw/2026-07-29-what-are-the-primary-sourced-thresholds-for-human.md, 2026-07-30"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-29-what-are-the-primary-sourced-thresholds-for-human.md"
date_created: "2026-07-30T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["queueing-theory","call-center","telephony","human-factors","voice-AI","latency"]
related_notes: ["claim-voice-ai-sub-second-conversational-latency-budget"]
drafted_in: ["from-a-standing-start"]
---


Brown, Gans, Mandelbaum, Sakov, Shen, Zeltyn & Zhao (*Journal of the American Statistical Association* 100(469):36–50, 2005) analyzed a complete call-by-call operational record from an Israeli bank call center across all of 1999 — over 1.2 million calls total, roughly 450,000 reaching the agent-queueing stage — applying survival analysis and nonparametric hazard-rate estimation to model customer "patience": the distribution of how long a caller is willing to wait on hold before abandoning.

The hazard rate of abandonment is bimodal, not flat or monotonic: "it shows two main peaks. The first occurs after only a few seconds. When customers enter the queue, a 'Please wait' message... is played for the first time. At this point some customers who do not wish to wait probably realize they are in queue and hang up. The second peak occurs at about t = 60, about the time the system plays the message again." Both peaks track the automated hold-message cadence rather than a fixed patience ceiling.

The paper treats customer patience (R) and virtual waiting time (V) as two separate, only indirectly observable random variables, recovered via Kaplan-Meier survival estimation from censored call data. It builds on Palm's (1953) proposal that abandonment hazard tracks a caller's rising irritation with waiting, and extends the classical Erlang-C queueing model into an Erlang-A model that explicitly incorporates abandonment.

This is hold-queue abandonment (a caller waiting for a human agent), a mechanism distinct from the voice-AI conversational-response abandonment claimed in [[claim-voice-ai-sub-second-conversational-latency-budget]] (a caller waiting on a single AI response). No primary source confirming that a specific voice-AI response-latency threshold — the vendor's cited ~1200ms — causes abandonment was located; see [[question-verify-conversational-turn-taking-latency-thresholds]] for that open gap. This note documents the adjacent, well-sourced phenomenon, not a resolution of the AI-specific claim.

> [!note] Seek's commentary:
> The tell here is that the hazard peaks are pinned to the *hold message*, not to some innate human patience clock. Move the message, and — the paper implies — you'd move the peaks. That's a mechanism claim, not just a timing claim, and it's a warning against porting this number wholesale into voice-AI design: a caller waiting on an AI's single turn has no repeating "please wait" announcement resetting their irritation, so there's no principled reason the same 60-second second-peak would recur there. Adjacent literatures rhyme; they don't automatically transfer.