C’s queuing question “Ok so you have some process you need to put customers through. And you know avg standard dev of their interarrival times. You also know the avg and standard deviation of service times (how long it takes you to serve them once you start serving them). You also know how many ppl you have serving customers. From this, you can calculate the average time a customer will wait before receiving service. “But can you calculate the standard deviation of that waiting time?”
Set parameters for interarrival distribution:
interarrivalMean = 200
interarrivalSD = 100
Set parameters for service time:
serviceMean = 1000
serviceSD = 200
Now we simulate:
Waiting = html`${unservedCustomers.map(c => c.char).join(' ')}`
BeingServed = html`${currentCustomers.map(c => c.char).join(' ')}`
Served = html`${servedCustomers.map(c => c.char).join(' ')}`
The wait times are:
waitTimeAvg = d3.mean(waitTimes)
waitTimeSd = d3.deviation(waitTimes)
Once being served, the service times are:
servingTimeAvg = d3.mean(servingTimes)
servingTimeSd = d3.deviation(servingTimes)
Here's a histogram of the wait times:
chart
Next step would be to try with different inputs and see how the standard deviation of wait time is affected. But it's late!
Showing my work
d3 = require('d3')
import {chart} with {waitTimes as data} from "@mbostock/d3-histogram@202"
servers = { let servers = this || d3.range(5).map(() => ({customerId: false, timeToComplete: false})) while (true) { servers.filter(s => s.customerId !== false).forEach(s => { if(Date.now() - customers[s.customerId].serving > s.timeToComplete) { customers[s.customerId].served = Date.now() s.customerId = false } }) servers.filter(s => s.customerId === false).forEach(s => { if(!s.customerId) { var index = customerIndexes.shift() if(index !== undefined) { s.customerId = index s.timeToComplete = service() customers[index].serving = Date.now() } } }) yield servers } }
customers = { let i = []; let chars = ['👦🏻','👦🏼','👦🏽','👦🏾','👦🏿','👧🏻','👧🏼','👧🏽','👧🏾','👧🏿','👨🏻','👩🏻','👱🏼','👩🏼'] while (true) { yield new Promise(resolve => { setTimeout(() => resolve((i.push({ arrived: Date.now(), char: chars[Math.floor(Math.random()*chars.length)] }), i)), interarrival()) }) } }
unservedCustomers = customers.filter(c => !c.served && !c.serving)
currentCustomers = customers.filter(c => c.serving && !c.served)
servedCustomers = customers.filter(c => c.served)
customerIndexes = customers.map((c,i) => !c.served && !c.serving ? i : false).filter(d => d !== false)
waitTimes.x = "Wait times"
waitTimes = customers.filter(c => c.serving).map(c => c.serving - c.arrived)
servingTimes = customers.filter(c => c.served).map(c => c.served - c.serving)
service = d3.randomNormal(serviceMean, serviceSD)
interarrival = d3.randomNormal(interarrivalMean, interarrivalSD)