Morning Surge Queue Analysis

Most polling places will face a surge of voters at some point during the day, often in the early morning. When many voters are lined up outside the polling place prior to the polls opening, it will take time before that line is expected to dissipate to zero. This tool helps understand what will happen during the time immediately after the polling place opens with a line already formed.

Use This Tool To:

  • Determine when the morning surge will dissipate
  • Determine how long lines will get during the surge

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Surge Dissipation Visualization

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Choose System Setup:

Polling Place Characteristics

Input Statistics Calculated Statistics
Task Number of Stations Average Time to Complete Task (min) Capacity (voters/hr) Utilization (%)
Check In

Voter Arrival Characteristics

Description Units Value
Voter Arrival Rate Voters/hr
Length at Start Voters


Surge Dynamics

The output shows how long you can expect it to take for the line to return to zero. It also shows how likely it is that the line will grow to at most a certain length before it diminishes to zero.
Description Units Value
Duration of Surge Hours
50% Chance Voters
75% Chance Voters
95% Chance Voters

Input Data Description

Polling Place Characteristics

  1. System Setup: Use the dropdown to change the polling place setup
  2. Number of stations: The number of voters who can be served simultaneously at each step in the process
  3. Average Times: The average time each voter spends at each station

Voter Behavior Characteristics

  1. Arrival Rate: The average rate (voters/hour) that arrive at the polling place after the polls open
  2. Line Length at Start of Voting: The length of the line prior to polls opening

Model Assumptions

This tool uses queueing theory to model the dissapation of a line given its downstream steps. This model is most easily thought of as studying the system in the early morning, immediately after opening the polls. We assume that there is an empty system (i.e. nobody in the polling place) and a built up line (i.e. some number of people waiting outside) prior to opening the system, at which point the line is worked down at the average processing rate, and voters continue to arrive at the average arrival rate.

The tool relies on a classic queuing model, known as an “M/M/k system.” For this model of a polling site, we assume that voters arrive randomly with a constant arrival rate, and join a single queue that is being served by a set of parallel stations or servers. In a polling site, we assume that we are modeling the bottleneck step in the process; this might be the check in stations, or the voting stations, or possibly the ballot scanning station or a health check.

This tool assumes that immediately after opening, the line length decreases by the number of stations in the bottleneck. It then reports the line lengths that the system has a 50%, 25%, and 5% chance of reaching prior to reaching no line.

This tool may be used to study a built up line in the middle of the day with a slight variation, see the instructional videos for more.

Developers: Stephen Graves and Colin McIntyre

© 2020 The Stanford-MIT Healthy Elections Project All rights reserved.