Queue wait time calculator
How long your customers wait in the peak hour, how many are standing in the queue, and whether one more counter would fix it — then the queue management system that fits.
Your counters
Three numbers give you the wait. The rest picks the system.
≈ 72 in the peak hour
Average time at the counter
In the peak hour
Separate token series — Cash, Loans, X-Ray
Of the day's visitors. Banks and OPDs run 15–20%.
The table marks the counters that get you there
One token printer or kiosk each
Each needs its own display
Indicative bill of materials
For LED Wired on 7 counters, 3 queues, 1 entrance. The site survey fixes the counts.
| Item | Qty |
|---|---|
| Counter calling unit7-segment readout, NEXT and CALL keys | 7 |
| Thermal token printer with auto-cutter and end sensor3 queue buttons | 1 |
| LED token display, 7 lines | 1 |
| Control box220 V here and at the printer | 1 |
| 6-core 14/38 multistrand cableclient scope, laid to our schedule | Lot |
| Thermal paper rolls (55 mm, end sensor) | Consumable |
- Power is needed only at the control box and the printer; the calling units and the display draw from the cable. The cable itself is laid by your electrician to our schedule.
Common to all three models and left out of the choice above: priority calling, queue merging, * next / # recall, midnight reset, voice announcement in Indian languages and a customised token print.
Email me this as a report
The wait-time table, the recommended system, what was ruled out and the bill of materials, formatted so a branch manager can send it to a regional head — plus a link that reopens this exact configuration.
Sales line +91 7975843985 · Mon - Sat, 09:30 - 18:30 IST
Queue wait-time report — Infra DigiTech Pvt Ltd
https://infra-digitech.com/tools/queue-wait-time-calculator?day=400&svc=5&ctr=7&q=3&cable=1
Inputs
400 visitors/day, 18% in the peak hour → 72/hour · 5 min per customer · 7 counters · 3 queues · Other counters
Wait at 7 counters
At 7 counters your customers wait about 3 minutes on average, with about 4 people in the queue at any moment. An 8th counter cuts that to under a minute.
| Counters | Wait | Queue | Load |
|---|---|---|---|
| 5 | overloaded | — | 120% |
| 6 | overloaded | — | 100% |
| 7 (now) | 3.1 min | 4 | 86% |
| 8 | <1 min | 1 | 75% |
| 9 | <1 min | 0 | 67% |
Recommended system
LED Wired — One 6-core cable, power at two points only
LED Wired fits 7 counters and 3 queues.
- One 6-core 14/38 multistrand cable — ordinary cable from any electrical market — carries the printer, every calling unit and the display, so power is needed at the control box and the printer only.
- Up to 8 display lines cover your 7 counters at once.
- Numbers-only calling with up to six queues on the thermal printer is exactly what this model is built for.
Indicative bill of materials
| Counter calling unit — 7-segment readout, NEXT and CALL keys | 7 |
| Thermal token printer with auto-cutter and end sensor — 3 queue buttons | 1 |
| LED token display, 7 lines | 1 |
| Control box — 220 V here and at the printer | 1 |
| 6-core 14/38 multistrand cable — client scope, laid to our schedule | Lot |
| Thermal paper rolls (55 mm, end sensor) | Consumable |
- Power is needed only at the control box and the printer; the calling units and the display draw from the cable. The cable itself is laid by your electrician to our schedule.
Infra DigiTech Pvt Ltd · Sales +91 7975843985 · [email protected] · https://infra-digitech.com/tools/queue-wait-time-calculator
Read the table, not the single number.
The headline wait is an average across a peak hour, and averages hide the shape of the problem. The table underneath is what to take to a regional head or a hospital administrator: it shows exactly what each extra counter buys, and where the curve flattens. Waiting time does not fall in a straight line as counters are added — it collapses. A branch at 90% counter load can be waiting twenty minutes; one more counter takes the load to 75% and the wait to six. The counter after that buys much less. The row marked "target" is the smallest counter count that gets under the wait you set, and the sentence above the table says the same thing in words.
The recommendation below the table is a separate question. The wait is about how many counters you open; the model is about what you need those counters to do — numbers or names on the screen, one token forwarded between departments, reports for the office, whether cable can be run. The ruled-out list names each model that cannot meet a requirement you set and the sentence that removed it, which is the part most useful when two quotations look identical.
Erlang C, the peak-hour assumption, and what is left out.
Nothing here is proprietary. The waiting-time model is the one telephone exchanges have been dimensioned with for a century, the peak-hour share is stated and adjustable, and the model rules are the published limits of the three systems we manufacture. A consultant can check any figure on this page by hand.
1. Arrivals
Most branch managers know daily footfall, not arrivals per hour, so the tool takes either.
λ = visitors per day × peak share — the peak share defaults to 18%, the busiest hour of a typical bank branch or OPD morning, and is adjustable. Or enter the peak-hour count directly.
μ = 60 ÷ minutes per customer — how many customers one counter serves in an hour.
2. The wait — M/M/c, Erlang C
With c counters, offered load a = λ ÷ μ erlangs and utilisation ρ = a ÷ c:
P(wait) = [aᶜ ÷ (c!·(1−ρ))] ÷ [Σₖ₌₀ᶜ⁻¹ aᵏ÷k! + aᶜ ÷ (c!·(1−ρ))]
W = P(wait) ÷ (c·μ − λ) is the average wait before being called, and L = λ·W is the number of people in the queue at any moment (Little's law). When ρ ≥ 1 the queue has no steady state — it grows for as long as the peak lasts — and the tool says so rather than printing a number.
The sums are built by recurrence rather than factorials, so the figures stay exact at fifteen or fifty counters.
3. Which system — elimination rules
A model with any blocker is ruled out and shown with every sentence that removed it, not just the first.
- 1Department or doctor names on the screen → both LED models are removed. They show numbers only.
- 2More queues than the model carries → removed. LED models take 6 on our thermal printer (2 on a POS printer); LCD is configurable to 100.
- 3More than 9 counters → both LED models are removed. LCD has no fixed counter limit.
- 4Token forwarding, mobile calling app, reports, SMS tokens, a second waiting area or a tab kiosk → both LED models are removed. These are LCD-only.
- 5Finished interiors → LED Wired is removed. It needs one 6-core cable to every unit.
4. Ranking the survivors
Points for how well each surviving model suits the site; the top scorer is recommended.
| Situation | Winner |
|---|---|
| Cable is possible, up to 6 queues and 9 counters, numbers on the screen Lowest cost, and 220 V is needed at only two points — the control box and the printer. | LED Wired |
| Finished interiors, up to 6 queues and 9 counters, numbers on the screen No cabling at all; runs on our own network with a 220 V point at each unit. | LED Wireless |
| Named queues, forwarding, app, SMS, reports, a tab kiosk, more than 6 queues or 9 counters, or a second waiting area Nothing else in the range does these. | LCD Wireless |
Limitations, stated plainly
- Arrivals are treated as random at a steady peak-hour rate. A bus-load at 10:05 or a lunch lull inside the hour makes the real wait bumpier than the average shown.
- One average service time covers every counter. A branch where the loans desk takes fifteen minutes and cash takes two is really two queues; run them separately.
- Counters are assumed open for the whole hour. Staff breaks, a counter closed for a training session or a system down for five minutes all add to the wait.
- The peak-hour share is an assumption until you count it. Once a system with reports is installed, your own token data replaces both the share and the service time.
Every system the calculator chooses between.
Waiting time, counters and which system.
How is the waiting time calculated?+
With the standard M/M/c queueing model — customers arrive at random at your peak-hour rate, each counter serves one at a time at your average service time, and the Erlang C formula gives the probability a customer has to wait and the average length of that wait. The number of people in the queue follows from Little's law. It is the same model telephone exchanges and call centres are staffed with, and it is written out in full on this page.
How many counters does a bank branch or OPD need?+
Enough that counter utilisation stays below roughly 85% in the peak hour; above that, waiting time rises steeply with every extra visitor. As a rule of thumb, divide peak-hour arrivals by the number a counter serves in an hour (60 ÷ minutes per customer) to get the load in erlangs, and open at least that many counters plus one or two for the randomness. The table on this page shows the exact wait at each counter count for your numbers.
I only know my daily footfall. How do you get arrivals per hour?+
By taking a share of the day as the busiest hour — 18% by default, which is what a bank branch or hospital OPD typically sees between 10 and 11 in the morning. You can change the share in the fine-tune section, or switch to entering the peak-hour count directly if you have counted it.
Which queue management system is right for a bank branch?+
If cable can be run and the branch calls numbers only, LED Wired is the lowest-cost fit and needs power at just two points. If the interiors are finished, LED Wireless does the same job without a cable. If the branch wants named queues — Passbook, Cash, Loans — or the regional office wants wait-time reports, that is the LCD Wireless model. The calculator applies these rules and says which model it removed and why.
Which queue management system is right for a hospital OPD?+
Almost always the LCD Wireless model, because an OPD patient moves — registration, consultation, lab, pharmacy — and only LCD forwards one token between counters and shows department or doctor names on the screen. A single-doctor clinic or a pharmacy window with one queue is served well by an LED model or a standalone token display.
Is the result a quotation?+
No. It is a sizing aid: the wait your counters produce, the counters that would bring it under your target, the model that meets your requirements and an indicative bill of materials. The emailed report carries a link that reopens the exact configuration so an engineer can pick it up from there.
Want an engineer to check the result?
Send the link. We read the same configuration you see, confirm the model against your counter layout and come back with a quotation and a site-survey date.