System Capacity Design
Queue based agent and repeater sizing for trunked radio and dispatch systems. Erlang C (M/M/c) with full queue performance metrics, N minus 1 redundancy, and busy hour scenario comparison.
Trunked radio systems, dispatch consoles, and control room communications behave fundamentally differently from blocking radio networks. When all channels are busy, a new call does not get a fast busy and disappear. It waits in queue until a channel frees up. The right capacity model is therefore not Erlang B but Erlang C, the M/M/c queue model. Sizing a queued system with a blocking model is a common and expensive mistake. It produces channel counts that look right on paper but deliver unacceptable wait times in service, particularly during the morning shift turnover, end of shift, or any incident response.
The noIM₃ Erlang C Calculator is a complete capacity planning workspace for queued communication systems. Three calculation modes cover sizing, capacity, and validation. Agents Required finds the minimum agent or channel count to meet a service level target (for example 80 per cent of calls answered within 20 seconds). Max Users finds the largest fleet a fixed channel plan can support at a given service level. SL Analysis evaluates service level and full queue performance for a known agent count and offered traffic. All three drive the same downstream outputs (repeater sizing, N minus 1 analysis, sensitivity sweep, scenario comparison) so switching modes is non destructive.
Queue performance is surfaced comprehensively rather than reduced to a single number. C(m, A) is the probability that an arriving call must queue. P(Immediate Answer) is its complement. Average Speed of Answer (ASA) is the mean wait across all calls including the ones that do not wait. Wq is the average wait for callers who do queue. Lq is the average number of callers waiting. P(W > T) is the probability that wait exceeds a configurable target threshold. Achieved service level is checked live against the target with a clear pass or fail indicator. Together they give the full picture of queue behaviour rather than the misleading impression that a single utilisation number can deliver.
Agents Required finds the minimum agent or channel count to meet a service level target. Max Users finds the largest fleet a fixed channel plan can support. SL Analysis evaluates service level and full queue performance for a known channel count and offered traffic. All three modes share the same downstream outputs, so switching modes is non destructive.
Every result surfaces the full Erlang C performance profile. Probability a call must queue (C of m and A). Probability of immediate answer. Average speed of answer across all calls. Average wait for queued callers. Average queue length. Probability wait exceeds a target threshold. Achieved service level with a live pass or fail indicator against the configured target.
Traffic can be entered directly or derived using the built in busy hour call attempts (BHCA) estimator. Three survey methods are supported. System level daily call counts with busy hour peaking. Per person calls per shift. Uniform distribution across shift hours. For mixed fleets such as operations, supervisors, and emergency users with different call patterns, the multi group aggregator accepts separate populations with individual BHCA, average hold time, and activity factor inputs. Weighted average hold time is calculated automatically and used throughout the queue model.
The N minus 1 panel models the impact of losing one repeater from the designed pool, recalculating service level and full queue performance under degraded conditions. Essential for trunked radio in critical infrastructure, public safety, and any environment where a single repeater outage cannot be allowed to push wait times past acceptable thresholds.
A sensitivity table sweeps offered traffic across a configurable range, showing required agents, repeaters, and service level at each load point. Identifies where queue performance degrades sharply (Erlang C systems often look healthy until utilisation passes 70 to 80 per cent, then collapse rapidly). Useful for validating design margin against projected user growth.
Define up to five named busy hour scenarios with independent user counts, BHCA, average hold time, service level targets, wait time thresholds, and growth margins. The comparison table shows offered traffic, required agents, agents with growth, repeaters, utilisation, achieved service level, and ASA side by side. The worst case scenario is automatically identified and flagged as the procurement driver.
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 and Tier III return two voice channels per repeater. TETRA returns four channels per repeater. Analog trunked returns one channel per repeater. Custom multipliers are supported. Output is a deployable repeater count rather than a raw channel number.
A reference Erlang C table is built in for cross checking results against published values. CSV export captures inputs, queue performance, model outputs, sensitivity sweep, and scenario comparison so the analysis can be filed against the project, attached to a procurement document, or submitted with a technical proposal.
Reach for the Erlang C Calculator in any of the following situations.
Erlang C is correct when blocked calls wait in queue for a free channel rather than being cleared. Trunked radio (DMR Tier III, P25 Phase II, TETRA), dispatch consoles, and control rooms are queued environments and need Erlang C. Conventional radio and analog systems where unanswered calls are immediately cleared are blocking environments and need Erlang B. Picking the wrong model produces sizing that looks right on paper but fails in service.
Service level is typically expressed as the percentage of calls answered within a target wait time, for example 80 per cent answered within 20 seconds (often written 80 / 20). Public safety and emergency services typically require tighter targets such as 90 / 10 or higher. Less critical operations may accept 70 / 30 or 80 / 60. The right target depends on operational expectation, the cost of a delayed call, and any contractual or regulatory commitment.
C(m, A) is the Erlang C probability that an arriving call must wait in queue, given m channels and offered traffic A. It is the foundation metric of the model. Probability of immediate answer is its complement (1 minus C(m, A)). Average speed of answer (ASA) and queue length both derive from C(m, A) combined with average hold time and channel count. Surfacing C(m, A) directly tells you how often the queue actually engages, not just the average wait.
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 mixed fleets, the multi group aggregator lets you define separate populations with individual BHCA, average hold time, and activity factor inputs, and weighted average hold time is computed automatically.
Yes. 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 and Tier III return two voice channels per repeater. TETRA returns four channels per repeater. Analog trunked returns one channel per repeater. Custom multipliers are supported.
This is the defining behaviour of Erlang C systems. Up to about 70 to 80 per cent utilisation, queue length grows slowly. Past that, queue length grows non linearly and service level can collapse over a small change in offered traffic. The sensitivity sweep makes this visible so you can size with margin rather than discovering the collapse during a real busy hour.
Yes. Up to five named scenarios with independent user counts, BHCA, average hold time, service level targets, wait time thresholds, and growth margins. The comparison automatically identifies the worst case as the procurement driver, so the agent and repeater count on the order survives every realistic peak rather than only the average day.
It recalculates service level and queue performance after losing one repeater from the designed pool. The intent is to confirm that a single repeater outage does not take service level below the contractual or operational threshold. Essential for critical infrastructure, public safety dispatch, and any environment where a single failure cannot be allowed to take the network down.
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