Single Queue vs Multiple Queues — Service Design

Q: Single Queue vs Multiple Queues — Service Design

This question evaluates competency in queueing theory, stochastic process modeling, service-design trade-offs, and empirical validation methods relevant to data scientists.

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Question

Bank Branch Queue Design: Single Line to c Tellers vs c Independent Lines

Context and assumptions for comparability:

Arrivals are approximately Poisson at rate λ customers per unit time.
Each teller serves with i.i.d. exponential service times with rate μ per teller (FCFS discipline).
No balking/reneging initially; we discuss them later.
Two designs:
1. Single serpentine line feeding the first available of c identical tellers (an M/M/c system).
2. c independent lines, one per teller, with customers choosing a line uniformly at random on arrival (equivalent to c parallel M/M/1 queues each with arrival rate λ/c). If customers perfectly choose the shortest line, performance improves but still generally trails a pooled single line under identical assumptions.

Questions

Compare the expected waiting time and its variance between the single-line multi-server system and multiple independent queues.
Under what customer-load scenarios does one system outperform the other?
How would you model customer experience and throughput analytically?
What data would you collect post-implementation to validate the design choice?

Single Queue vs Multiple Queues — Service Design

Bank Branch Queue Design: Single Line to c Tellers vs c Independent Lines

Questions

Solution

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