System Capacity Design
Size channels and repeaters for radio systems where blocked calls are cleared, with Erlang B, Engset and Extended Erlang B compared side by side.
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Walkthrough
The three calculation modes and the main results.
Overview
Capacity is where many radio system designs quietly go wrong. A repeater count chosen by rule of thumb can look fine on an average day, then block calls at shift change or during an incident when traffic peaks. Sizing the system properly means applying a traffic model to how the users actually call. For systems where a blocked call is cleared and the user tries again later, that model is Erlang B.
The noIM₃ Erlang B Calculator works in three modes. It finds the channels needed to meet a grade of service target, the largest fleet a fixed channel count can support, or the blocking probability of a known design. The channel count is converted into a repeater count for the chosen radio technology, allowing for a growth margin and any control channel reserve.
Erlang B assumes a large user population, which is not always true. Engset uses the actual number of users, which matters when it is small, and when blocked callers retry straight away, Extended Erlang B accounts for the extra traffic. The calculator shows all three models side by side, with the channels each needs.
Channels Required finds the minimum channel count that meets a grade of service target. Max Users finds the largest fleet a fixed channel count can support. GOS Analysis reports the blocking probability for a known channel count and traffic load.
Every result is checked against Erlang B, Engset and Extended Erlang B. Engset uses the user count you enter, and Extended Erlang B applies when you enter a retry rate for blocked callers, finding the channels at which the blocking with retries meets the target. The comparison shows how much the model choice changes the answer.
Offered traffic is worked out from the number of users, busy hour call attempts, call duration and an activity factor. An estimator helps when you only know daily call counts or calls per shift, and a multi-group aggregator combines user groups with different call patterns.
The channel count is converted into a repeater count for analogue, P25 Phase I or II, DMR Tier II or III, TETRA, or a custom number of voice paths per repeater. Growth is applied to the traffic and the channels are solved again, then a control channel reserve is added before the repeater count is rounded up.
The redundancy check removes one repeater, and then two, from the design and recalculates the blocking. Each result is compared with your grade of service target, at the design traffic including growth, so you can see whether the system still meets it after a repeater failure.
A sensitivity table shows how the channels, repeaters or blocking change as traffic grows. Named busy hour scenarios with their own users, call rates, targets and growth margins are compared side by side, and the worst case is marked as the one that drives procurement.
Charts plot blocking against traffic and channel count, along with dimensioning and utilisation curves. An Erlang B reference table and a step by step calculation breakdown make each result easy to check.
Calculations run in your browser. Projects can be saved to your account, and results can be exported to CSV or copied to the clipboard for a design report.
Inputs and outputs
Inputs 12
Outputs 11
Use cases
Erlang B assumes a large user population and suits systems with many users per channel. Engset is more accurate when the number of users is small compared with the number of channels, where Erlang B can understate the blocking. Extended Erlang B suits systems where blocked callers retry straight away, which adds to the offered traffic. The calculator shows all three so the choice is an informed one.
Grade of service is the probability that a call is blocked because no channel is free. There is no single standard figure: the right target depends on user expectations, the cost of a blocked call and any contractual obligations.
The busy hour estimator works from a system daily call count with a busy hour peaking factor, from calls per person per shift with a peaking factor, or from calls spread evenly across a shift. For mixed fleets, the multi-group aggregator takes separate user groups with their own call rates, durations and activity factors, and combines them into one offered traffic figure.
Each technology carries a set number of voice paths per repeater: one for analogue and P25 Phase I, two for P25 Phase II and DMR, and four for a TETRA carrier. You can also set a custom figure. The calculator adds the growth margin and any control channel reserve, then rounds up to a whole number of repeaters.
It recalculates the blocking after removing one repeater's voice paths from the design, and again after removing two. Each result is rated against grade of service thresholds you set, so you can see whether a repeater failure would push blocking past an acceptable level.
No. Erlang B is for systems where blocked calls are cleared. When calls wait in a queue for a free channel, as in many trunked radio and dispatch systems, the Erlang C model applies. Use the noIM₃ Erlang C Calculator for those systems.
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