Staffing and Service Models

Once workload has been calculated and a speed of answer objective established, staffing numbers can be calculated. Due to the random arrival of calls and the fact that some callers will find no agent available, it is not simple to match workload with a given number of staff. Finding the right number of staff involves the use of detailed mathematical models that replicate the unique staffing issues of the call center.

There are several mathematical models that are used in telephone traffic engineering applications. Some of these are particularly suited to the unique operational aspects of the call center. The primary traffic models associated with call center operations are:

• Erlang C
• Erlang B
• Erlang Engset
• Equivalent Random TheoryThese four models represent traffic engineering models that are used in a variety of telephone related engineering situations. Most of these are Erlang traffic model as a foundation. A.K. Erlang, a Danish mathematician who worked for the Copenhagen Telephone Company in the early 1900s, developed these techniques. These mathematical models are based on the arrival rates and usage patterns is telephone calling and there are variations of the Erlang formulae to equate with different types of telephone situations. The most common ones used in call centers are discussed below.

Erlang C Model

Most call center used a model called Erlang C to determine resource requirements to handling incoming calls. The assumptions behind the Erlang C model are that the events (or calls) arrive randomly within the work period (hour or half hour). The Erlang C model also assumes that if a calls attempt is made and no resource (in this case, a call center agent) is in place to handle the call, the call will go into a queue and wait there until there is a resource to handle it. It is the model used most frequently in a simple call center scenarios where a caller is asked to hold for the first available agent when entering the queue,

Formula and Tables

The formula for Erlang C is somewhat complex, and it is difficult to calculate staffing requirements and delay information using a pencil and calculator. The formula is as follows:

The Erlang C formula has been used to create Erlang C tables which can be used to determine the number of resources required to meet a certain service goal, or to determine a resulting delay statistic if the number of resources is given below table contains an excerpt of an Erlang C table for 20 hours of telephone workload.

The steps of using and Erlang table are as follows:

1. Calculate Staff WorkloadFor this example, assume 300 calls per hour with an average handle time of 4 minutes per call, equating to 1200 minutes or 20 hours of workload.
2. Determine a Service Objective. For this example, assume that the call center wants the callers that go into queue to wait there no longer than 45 seconds. In order to look up this service goal in a standard Erlang C table, the wait time would be translated into a Delay Length Call Factor (DLCF). The DLCF is a factor or ratio that compares, the desired wait time to the average call length. In this example, the desired wait time (45 seconds) compared to the average handle time (240 seconds) equals 187 (45/240 = .187).
3. Determine Service RequirementsThe DLCF calculated in Step 2 is then used to determine the number of staff needed. Note in the table where DLCF is equal to or less than .187 to determine the number of resources (staff) needed. In this example, the required number of resources would be 26 staff, since the DLCF of .167 is the number that comes closest to and is less than the DCLF requirement.
4. Calculate Actual DelayThe actual time the delayed callers spend in queue can now be calculated. Multiply the DLCF value found in the table (.167) by the average handle time of 240 seconds to determine the actual wait time for the callers that go into queue. With 26 staff, the delay of delayed callers will be 40 seconds (.167 x 240 sec)
5. Calculate Average Delay of the all callsThe Erlang C table also provides a statistics that shows what percentage of the calls will actually go into queue, called the delayed portion. With 26 staff in place, the delayed portion is .143, meaning that 14.3% of calls will go into queue and wait there an average of 40 seconds. The other 85.7% of calls will not experience a delay and the wait time of those calls will be zero seconds. The weighted average of these two groups [(.143 x 40)] + (.857 x 0 )] yields the average delay of all calls, typically referred to as the average speed of answer or ASA. In this example, the ASA would be 5.72 seconds of delay.

Erlang C Software Tools

The Erlang C model is used as the basis for many call center staffing tools. The staffing tool used to calculate the examples is called QuickStaff - a call center resource planning tool developed and distributed by the call center school. (Note: The QuickStaff tool is available for download from www.callcenterschool.com.) This tool uses the Erlang C model to calculate required resources if workload and service goals are known, or conversely to calculate the service statistics with workload and staff numbers as input.

Thanks,

With Love and Sincerity,

Contact Center Workforce Management and Quality Optimization Specialist.