Erlang B and Erlang C for voice and contact center sizing

Sources

1. 1
   Cisco defines average handle time as the mean call duration over a period; it is the sum of handling-time types such as call treatment time for self-service calls or talk time for agent calls.

   Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Average Handle Time (AHT) · Checked 2026-09-25
2. 2
   Hong et al. report empirical evidence that arrivals in large service systems show over-dispersion (variance above Poisson), and state that under over-dispersion the square-root safety rule leads to understaffing.

   Staffing under Taylor's Law: A Unifying Framework for Bridging Square-root and Linear Safety Rules · Section 1 Introduction · Checked 2026-09-25
3. 3
   In Cisco's traffic model comparison, Engset assumes a smooth arrival pattern; EART/EARC and Neal-Wilkerson assume peaked arrivals; Poisson, Erlang B, Extended Erlang B and Erlang C assume random arrivals.

   Traffic Analysis · Traffic Models > model comparison table · Checked 2026-09-25
4. 4
   BHCA (busy hour call attempts) is the total number of calls attempted or received in the contact center during the peak traffic hour or interval.

   Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Busy Hour Call Attempts (BHCA) · Checked 2026-09-25
5. 5
   Worked example: 600 calls in the busy hour averaging 2 minutes each is a busy hour traffic load of 20 erlangs.

   Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Busy Hour Traffic (BHT) in Erlangs, example · Checked 2026-09-25
6. 6
   Busy hour traffic in erlangs is BHCA multiplied by average handle time in seconds, divided by 3600 (equivalently BHCA times AHT in minutes divided by 60).

   Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Busy Hour Traffic (BHT) in Erlangs · Checked 2026-09-25
7. 7
   Cisco's 2001 Traffic Analysis document states that in a standard business environment the busy hour carries about 15 to 20 percent of the day's traffic, and that 17 percent of daily traffic is generally used to represent the peak hour.

   Traffic Analysis · Traffic Theory Basics > Busy Hour Traffic · Checked 2026-09-25
8. 8
   Cisco's UCCX 15.0 guide describes the busiest hour as typically the average of the ten busiest hours of the year, and notes that seasonal campaigns may need a different staffing approach.

   Solution Design Guide for Cisco Unified Contact Center Express, Release 15.0 - Sizing Operating Conditions for Reference Design · Contact Center Basic Traffic Terminology > Busy Hour or Busy Interval · Checked 2026-09-25
9. 9
   Cisco's UCCX 15.0 design guide allows a busy interval of one hour or less, such as 30 or 15 minutes, when sizing is wanted for those shorter intervals.

   Solution Design Guide for Cisco Unified Contact Center Express, Release 15.0 - Sizing Operating Conditions for Reference Design · Contact Center Basic Traffic Terminology > Busy Hour or Busy Interval · Checked 2026-09-25
10. 10
    Cisco lists the inputs for Erlang calculators as BHCA, average handle time for each resource, service level (percentage answered within x seconds), and the grade of service (percent blockage) wanted for trunks and VRU ports.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang Calculators as Design Tools > required inputs list · Checked 2026-09-25
11. 11
    One CCS (centum call second) is 100 seconds of calls on the same circuit, and 1 erlang equals 36 CCS; voice switches generally measure traffic in CCS.

    Traffic Analysis · Traffic Theory Basics > CCS · Checked 2026-09-25
12. 12
    Daw, Pache and Zhou argue that Erlang-A guidance, which treats abandoning callers as lost forever, understaffs call centers where callers redial. For one SNAP call center it recommended 13 staff for an average wait under one minute, against 52 in their model.

    Due Process on Hold: A Queueing Framework for Improving Access in SNAP · Table 2 and surrounding discussion · Checked 2026-09-25
13. 13
    The Erlang-A queue (M/M/c+M) adds exponential customer abandonment at rate theta to the M/M/c model; with theta set to zero it becomes the Erlang-C queue.

    The Number of Overlapping Customers in Erlang-A Queues: An Asymptotic Approach · Section 2 (model definition) · Checked 2026-09-25
14. 14
    The Erlang B model as Cisco describes it assumes random call arrival, and when all trunks or ports are occupied new calls are lost or blocked (busy tone) rather than queued.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang-B Model > assumptions · Checked 2026-09-25
15. 15
    Cisco's Traffic Analysis document lists the Erlang B assumptions as an infinite number of sources, a random traffic arrival pattern, blocked calls cleared, and exponentially distributed hold times.

    Traffic Analysis · Traffic Models > Erlang B · Checked 2026-09-25
16. 16
    The Erlang B blocking probability for offered traffic E erlangs on m circuits is (E^m/m!) divided by the sum of E^i/i! for i from 0 to m. It can be computed by the recursion B(E,0)=1 and B(E,j)=E*B(E,j-1)/(E*B(E,j-1)+j).field report

    Erlang (unit) · Erlang B formula section · Checked 2026-09-25
17. 17
    The Erlang B formula holds for any holding-time distribution with a finite mean, even though it is usually derived assuming exponential holding times; Poisson arrivals are still assumed.field report

    Erlang (unit) · Erlang B formula section · Checked 2026-09-25
18. 18
    Erlang B relates three quantities (busy hour traffic, grade of service and number of ports or lines); given any two, the model calculates the third.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang-B Model > input and output factors · Checked 2026-09-25
19. 19
    Cisco directs designers to use the Erlang B model to size PSTN trunks, gateway ports and VRU ports.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang-B Model · Checked 2026-09-25
20. 20
    Cisco's Traffic Analysis document says the Erlang C model is more commonly used for conservative automatic call distributor (ACD) design, to find the number of agents needed.

    Traffic Analysis · Traffic Models > Erlang C · Checked 2026-09-25
21. 21
    The Erlang C model as Cisco describes it assumes random call arrival, and when all agents are busy incoming calls are queued rather than blocked.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang-C Model > assumptions · Checked 2026-09-25
22. 22
    Cisco's Traffic Analysis document lists the Erlang C assumptions as an infinite number of sources, a random traffic arrival pattern, blocked calls delayed, and exponentially distributed hold times.

    Traffic Analysis · Traffic Models > Erlang C · Checked 2026-09-25
23. 23
    The Erlang C probability that an arriving call must wait, for E erlangs on m agents, is (E^m/m!)(m/(m-E)) divided by [the sum of E^i/i! for i from 0 to m-1, plus (E^m/m!)(m/(m-E))].field report

    Erlang (unit) · Erlang C formula section · Checked 2026-09-25
24. 24
    Cisco lists the Erlang C inputs as the number of calls agents answer in the busy hour (BHCA), average talk time plus wrap-up time, and the delay or service level wanted, given as a percentage of calls answered within a set number of seconds.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang-C Model > input parameters · Checked 2026-09-25
25. 25
    Because the Erlang C formula contains m/(m-E), it only gives a meaningful result when there are more agents than offered erlangs. At 100 erlangs, as in NICE's example, a steady-state Erlang C answer needs more than 100 agents on the phones before shrinkage.inferred

    Erlang (unit) · Erlang C formula section (m/(m-E) term) · Checked 2026-09-25
26. 26
    The Erlang C model's outputs are the number of agents required, the percentage of calls delayed because no agent is available, and the average queue time.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang-C Model > output · Checked 2026-09-25
27. 27
    Because Erlang C assumes no caller abandons, it tends to call for more agents than an abandonment-aware model (Erlang A) for the same waiting target when abandonment is material. Redials push the other way.inferred

    The Number of Overlapping Customers in Erlang-A Queues: An Asymptotic Approach · Section 2 (theta = 0 reduction) · Checked 2026-09-25
28. 28
    Cisco directs designers to use the Erlang C model to size agents in contact centers that queue calls before presenting them to agents.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang-C Model · Checked 2026-09-25
29. 29
    Worked example: 30 calls of 6 minutes each in the busy hour is 180 minutes of traffic, or 3 erlangs.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Erlang, example · Checked 2026-09-25
30. 30
    One erlang is a traffic load equal to 3600 seconds of calls on the same circuit, trunk or port during the busy hour, i.e. enough traffic to keep one circuit busy for one hour.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Erlang · Checked 2026-09-25
31. 31
    Worked example: an outbound trunk group offered 17 erlangs in the busy hour and designed for under 1% blockage needs 27 circuits, which gives a grade of service of 0.64 percent.

    Traffic Analysis · Traffic Models > Erlang B > Example (17 erlangs outbound trunk group) · Checked 2026-09-25
32. 32
    Cisco's Extended Erlang B example assumes that 50 percent of blocked users retry immediately. Extended Erlang B is Erlang B with blocked calls retried instead of lost.

    Traffic Analysis · Traffic Models > Example 2: Using the Extended Erlang B Traffic Model · Checked 2026-09-25
33. 33
    Genesys Cloud lists service goals (SL/SLO, ASA, abandonment rate) that are more demanding than what was historically achieved as a cause of higher-than-expected staffing requirements.

    Why are staffing requirements higher or lower than expected? · Higher than expected staffing requirement · Checked 2026-09-25
34. 34
    Cisco describes 1% blockage (P.01) as a typical grade of service for PSTN trunks, noting that other applications may need different grades of service.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Grade of Service (Percent Blockage) · Checked 2026-09-25
35. 35
    Grade of service (percent blockage) is the probability that a resource is busy during the busy hour so that a call is lost or blocked; a grade of service of 0.01 means 1% of busy-hour calls are blocked.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Grade of Service (Percent Blockage) · Checked 2026-09-25
36. 36
    Wikipedia's Erlang (unit) article says that in high-loss systems, where heavy congestion produces re-entrant (retry) traffic, the Erlang formulas fail to predict the number of circuits needed.field report

    Erlang (unit) · Extended Erlang B / limitations discussion · Checked 2026-09-25
37. 37
    ITU-T Recommendation E.520 (11/88), in force, covers the number of circuits to provide in automatic and/or semiautomatic operation for circuit groups without overflow facilities.

    E.520 : Number of circuits to be provided in automatic and/or semiautomatic operation, without overflow facilities · Recommendation landing page: title and status fields · Checked 2026-09-25
38. 38
    ITU-T Recommendation E.521 (11/88), in force, covers calculating the number of circuits in a group that carries overflow traffic.

    E.521 : Calculation of the number of circuits in a group carrying overflow traffic · Recommendation landing page: title and status fields · Checked 2026-09-25
39. 39
    Cisco says the right traffic model depends on three factors: traffic source characteristics (finite or infinite), how lost calls are handled (cleared, held or delayed), and the call arrival pattern (random, smooth or peaked).

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Erlang Calculators as Design Tools · Checked 2026-09-25
40. 40
    In Cisco's traffic model comparison, all of Poisson, Erlang B, Extended Erlang B, Erlang C, EART/EARC and Neal-Wilkerson assume infinite sources and Engset assumes finite sources. Blocked calls are held (Poisson), cleared (Erlang B, Engset, EART/EARC), retried (Extended Erlang B) or delayed (Erlang C).

    Traffic Analysis · Traffic Models > model comparison table · Checked 2026-09-25
41. 41
    NICE's glossary works an example of 1,200 calls per hour at a 5-minute AHT, giving 6,000 minutes or 100 erlangs of workload, with Erlang C baseline staffing of about 110 agents; the example states no service level target.

    WFM Glossary · WFM Glossary > Baseline Staffing, example · Checked 2026-09-25
42. 42
    NICE CXone WFM defines baseline staffing as the minimum number of agents needed for expected workload under normal conditions, before shrinkage, variability or unexpected events are taken into account; required staffing is baseline plus shrinkage adjustments.

    WFM Glossary · WFM Glossary > Baseline Staffing · Checked 2026-09-25
43. 43
    NICE CXone WFM defines occupancy as the percentage of logged-in available time that agents spend handling customer interactions.

    WFM Glossary · WFM Glossary > Occupancy · Checked 2026-09-25
44. 44
    Offered traffic is the traffic that would be carried if every call attempt succeeded. Carried traffic is the average number of concurrent calls measured over a period; carried traffic is less than offered by the blocked portion.field report

    Erlang (unit) · Traffic measurements / offered traffic section · Checked 2026-09-25
45. 45
    For peaked call arrival patterns, Cisco suggests rollover trunk groups in some cases but says that in general enough resources must be allocated to handle the peak traffic.

    Traffic Analysis · Traffic Model Selection Criteria > Peaked Call Arrival Pattern · Checked 2026-09-25
46. 46
    Service level is the percentage of offered call volume that is answered within X seconds.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Service Level · Checked 2026-09-25
47. 47
    Cisco gives example service level goals of 90% of calls answered in under 10 seconds for sales and 80% of calls answered within 30 seconds for support centers.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Service Level · Checked 2026-09-25
48. 48
    Cisco states that the service level goal determines not only the agents needed but also the percentage of queued calls, the average time in queue, and the PSTN trunks and VRU ports needed.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Agent Staffing & Queuing > general principles · Checked 2026-09-25
49. 49
    The square-root safety staffing rule, which descends from Erlang C, staffs above the nominal load (arrival rate over service rate) by a safety margin proportional to the square root of the arrival rate in order to meet a delay-probability target.

    Staffing under Taylor's Law: A Unifying Framework for Bridging Square-root and Linear Safety Rules · Section 1 Introduction; Section 2 Example 2.1 · Checked 2026-09-25
50. 50
    In Cisco's contact center sizing terminology, talk time includes time the caller spends on hold and time spent in consultative conferences.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Talk Time · Checked 2026-09-25
51. 51
    The agent capacity figures in the Cisco UCCE 15.0(1) reference designs assume up to 30 calls per hour per agent.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Dynamic Configuration Considerations > BHCA Impact · Checked 2026-09-25
52. 52
    Cisco notes that VRU queuing and VRU self-service scenarios each need a different number of VRU ports because each has a different average handle time and possibly a different call load.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · VRU Port Sizing for Queuing · Checked 2026-09-25
53. 53
    Wrap-up (after-call work) time is the time after the caller disconnects that the agent spends completing tasks such as database updates and call documentation.

    Solution Design Guide for Cisco Unified Contact Center Enterprise, Release 15.0(1) - Sizing and Operating Conditions for Reference Designs · Contact Center Traffic Terminology > Wrap-Up Time (After-Call Work Time) · Checked 2026-09-25

Documents

Cite this page

WarmTransfer. (2026, September 25). Erlang B and Erlang C for voice and contact center sizing. WarmTransfer. https://warmtransfer.net/knowledge/erlang-traffic-engineering

@misc{warmtransfer-erlang-traffic-engineering,
  title  = {Erlang B and Erlang C for voice and contact center sizing},
  author = {{WarmTransfer}},
  year   = {2026},
  url    = {https://warmtransfer.net/knowledge/erlang-traffic-engineering},
  note   = {Verified 2026-09-25}
}