System Capacity Design
Repeater and channel sizing for blocking radio systems. Erlang B, Engset, and Extended Erlang B models with N minus 1 redundancy, busy hour scenario comparison, and technology aware sizing for P25, DMR, TETRA, and analog fleets.
Capacity planning is where most radio system designs quietly go wrong. A repeater count is chosen by rule of thumb early in the project, the licence is applied for, the radios are bought, and the network goes live. The complaints start a few months later when the morning shift turnover or an emergency response pushes traffic past the silently assumed busy hour, calls start blocking, and operators reach for new spectrum or extra repeaters that should have been planned in from the start. The right answer is not guesswork. It is Erlang B, applied properly to the actual user behaviour.
The noIM₃ Erlang B Calculator is a complete capacity planning workspace for radio systems operating under blocking conditions, where calls that cannot be served are cleared rather than queued. It runs three industry traffic models simultaneously. Standard Erlang B (ITU E.501) for the infinite population assumption used in most published tables. Engset for finite user populations where the user to channel ratio falls below ten and Erlang B starts to materially understate the required channels. Extended Erlang B for systems with significant retry behaviour, where blocked callers immediately try again and inflate the effective offered traffic.
Three calculation modes cover every sizing question. Channels Required finds the minimum channel count to meet a grade of service target. Max Users finds the largest fleet a fixed channel plan can support. GOS Analysis evaluates blocking probability for a given channel count and offered traffic. All three modes drive the same downstream outputs (repeaters, utilisation, N minus 1 analysis, sensitivity sweep, scenario comparison) so switching modes is non destructive. Outputs are technology aware for P25 Phase I and II, DMR Tier II and III, TETRA, analog, and custom systems, returning a deployable repeater count rather than a raw channel number.
Channels Required, Max Users, and GOS Analysis. The first finds the minimum channel count to meet a grade of service target. The second finds the largest fleet a fixed channel plan can support. The third evaluates blocking probability for a given channel count and offered traffic. All three drive the same downstream outputs, so switching modes is non destructive.
Every result is automatically cross checked against Erlang B, Engset, and Extended Erlang B. Engset activates a recommendation when the user to channel ratio falls below ten and Erlang B starts to materially understate required channels. Extended Erlang B iterates the effective offered traffic upwards to account for retry behaviour with a configurable retry fraction. The model comparison panel shows all three side by side so engineers can document the rationale for the model chosen.
Traffic can be entered directly or derived using the built in busy hour call attempts (BHCA) estimator, which supports three survey methods. System level daily call counts with busy hour peaking. Per person calls per shift. Uniform distribution across shift hours. For heterogeneous fleets, the multi group aggregator accepts separate user populations with individual BHCA, average hold time, and activity factor inputs and computes aggregate offered traffic automatically.
The N minus 1 panel models the impact of losing one repeater from the designed pool, recalculating blocking probability and flagging whether the degraded system remains within an acceptable grade of service. Essential for critical infrastructure, public safety, and any network where a single repeater outage cannot be allowed to take the service down.
A sensitivity table sweeps offered traffic across a configurable range, showing required channels, repeaters, and blocking at each load point. Lets planners identify the tipping points where adding one more user or one more channel changes the system materially, and validates the design margin against expected growth.
Define up to five named busy hour scenarios with independent user counts, BHCA, average hold time, grade of service targets, and growth margins. The comparison table shows offered traffic, required channels, channels with growth, repeaters, utilisation, and actual GOS side by side. The worst case scenario is automatically identified and flagged as the procurement driver, so the radio count on the order is the one that survives every realistic peak rather than just the average day.
Channel to repeater translation is technology aware. P25 Phase I returns one channel per repeater. P25 Phase II returns two voice channels per repeater. DMR Tier II returns two voice channels per repeater. TETRA returns four channels per repeater. Analog returns one channel per repeater. Custom multipliers are supported. The output is a deployable repeater count rather than a raw channel number that still needs translating.
A reference Erlang B table is built in for cross checking results against published values. CSV export captures the inputs, results, model comparison, sensitivity sweep, and scenario comparison so the analysis can be filed against the project, attached to a procurement document, or submitted with a spectrum licence application.
Reach for the Erlang B Calculator in any of the following situations.
Erlang B assumes an infinite user population and is appropriate when the user to channel ratio is high (greater than ten). Engset is the correct model when the user population is small relative to channel count, where Erlang B materially understates required channels. Extended Erlang B is appropriate when blocked callers immediately retry, which inflates the effective offered traffic. The calculator runs all three on every result so the model choice is informed rather than blind.
Grade of service is the probability that an arriving call is blocked because no channel is available. Common targets are 1 per cent for general purpose radio, 2 per cent for less critical operations, and 0.5 per cent or lower for public safety and emergency services. The right target depends on user expectation, the cost of a blocked call, and licence or contractual obligations.
The built in BHCA estimator supports three approaches. Enter system level daily call counts with a busy hour peaking factor. Enter per person calls per shift. Or enter uniform distribution across shift hours. For heterogeneous fleets, the multi group aggregator lets you define separate populations with individual BHCA, average hold time, and activity factor inputs.
Yes. The output respects technology specific channel to repeater multipliers. P25 Phase I returns one channel per repeater. P25 Phase II returns two voice channels per repeater. DMR Tier II returns two voice channels per repeater. TETRA returns four channels per repeater. Analog returns one channel per repeater. Custom multipliers are supported.
N minus 1 means the system continues to operate within an acceptable grade of service after losing one repeater from the designed pool. The analysis recalculates blocking probability with the reduced channel count and flags whether the degraded system still meets the target. Essential for critical infrastructure where a single outage cannot take the service down.
Yes. You can define up to five named scenarios (for example morning shift, evening peak, emergency response, end of month, summer storm) with independent user counts, BHCA, average hold time, grade of service targets, and growth margins. The comparison automatically identifies the worst case scenario as the procurement driver so the radio count on the order survives every realistic peak.
No. Erlang B is the correct model for blocking systems where unanswered calls are cleared. For queued systems where calls wait for a free channel, the Erlang C model applies. Use the noIM₃ Erlang C Calculator for queued environments such as call centres or systems with hold queues.
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