Workload Model for Asynchronous Channels

Workload Model for Asynchronous Channels is the capacity model for work that arrives, waits and is completed within a goal measured in hours or days rather than seconds: email, cases, tickets, claims and the other deferred queues of a service operation. It replaces the interval-by-interval delay calculation of a synchronous channel with a straight workload calculation: the items to be completed in a period, multiplied by the handling time per item, divided by the productive time one agent contributes to the channel in that period, with the open backlog rolled forward. It matters because a function that sizes an email queue with the telephony instrument gets an answer that is precise, confident and wrong in a way the instrument cannot report. The model is part of the Workforce Data Definitions Framework. Average Handle Time, Occupancy, Erlang C and Little's Law Applied to WFM keep their definitions on their own pages, and Back Office and Knowledge Worker Workforce Management describes the planning discipline of which this model is the arithmetic core.

The model's standing should be stated plainly. The peer-reviewed staffing literature is a literature of telephone queues and of a deferrable class sharing agents with a delay-constrained class; the research behind this cluster found no peer-reviewed closed-form staffing model for deferred work with a time-to-close goal. The workload model is therefore the practitioner model, not yet validated in the literature: its arithmetic is established, its use as a staffing method is inferred, and a practitioner source states the rule in the same terms, that email is sequential workload and the staff needed is equivalent to the workload hours. A page that calls it the standard method overstates it.

The work-item lifecycle

An asynchronous item passes through six events. Each needs a time stamp; an event with no instrument to stamp it is a gap the Source of Truth Register records.

Event	What it marks	Time stamp	Stamped by
Arrive	the item enters the function's perimeter	arrival	the work-item tool or mail system; for agent-created items, the creation action
Queue	the item waits unassigned, or assigned but untouched	queue entry and exit	the work-item tool where it routes; otherwise inferred as arrival to first touch
Open	an agent takes the item into work for the first time	first-touch start	the tool's assignment or status change; a desktop instrument's focus event
Touch	a bounded span of agent attention; an item may have several	each touch start and end	a work-item timer, a desktop focus instrument, or an agent-set state (Email Handle Time Measurement)
Pend	the item waits on a third party or the customer with no agent attention	pend start and end	the tool's status; where absent, the gap between touches is ambiguous between pend and idle
Close	the item is fulfilled; the unit of production is counted	close	the tool's status change; the one stamp almost every tool holds

Two durations are read off these stamps and are never the same number. Elapsed time is close minus arrive: the customer's clock, the quantity a time-to-close goal is measured on. Handling time is the sum of the touch durations (register entry AHT-02, RG-008, sourced from ST-007): the agent's clock, the quantity the requirement is computed on. The difference is queue time plus pend time plus idle time inside an open item. A tool that holds only arrive and close can report elapsed and cannot report handling, and using the first in place of the second is the most common error in asynchronous capacity models [A].

Two units of production per item

Every item produces two units, and a model needs both.

The count is one item fulfilled, stamped at close. It is the production unit of the channel, the quantity demand is forecast in, and the row the register's contact definition extends to asynchronous work. It is measured [M] wherever the tool stamps a close, which is nearly everywhere.

The time is the handling minutes the item consumed, the sum of its touches. It is the conversion factor from the count to hours, measured [M] only where touches are captured per item and otherwise estimated [E] from a state timer, a sampling study or an inference; the grade travels with it into every hour and full-time equivalent computed from it (Workload Units and the Roll-Up to FTE).

A count without a time cannot be rolled to hours; a time without a count cannot be checked against demand. Together they make test T-05, item count against time, on Reconciliation Tests for Time Accounting possible: items closed multiplied by handling time per item must sit inside the productive time the Agent Time Accounting Model records for the channel.

Backlog and ageing

Deferred work accumulates. The backlog is a stock, and its accounting is the most firmly established part of the model:

backlog at end of period = backlog at start + arrivals − closures, with closures bounded by capacity

Little's Law, L = λW, relates the stock to the mean time in system for a stable system in the long run, which gives two planning consequences and one limitation. When throughput is steady, the mean age of queued work is about the backlog divided by the throughput, an application of the law rather than a statement of it. A backlog that grows period after period means demand exceeds capacity, whatever an average over the quarter says; that is the stability condition. The limitation is that the law gives a mean only, and a goal of the form x percent of items closed within y hours is a statement about the tail of the age distribution, which the law does not supply. The model therefore carries an ageing profile, the count of open items by age bucket at the end of each period, read from the arrive stamp. The profile, not the mean, is what the goal is checked against.

The requirement

For a period, which is a shift or a day and never a fifteen-minute interval:

required productive hours = Σ over item types (items × handling minutes per item ÷ 60) + backlog hours to clear + variability buffer

required agents = required productive hours ÷ productive hours per agent per period

Productive hours per agent are read from the ledger: scheduled hours less shrinkage, with SHR-01 computed here on the scheduled-hours denominator so that the subtraction stays within one ledger tier, less in-work time on other channels, which is where a blended agent's voice time leaves the email calculation rather than being counted twice. The backlog term is the share of the opening backlog the function intends to clear this period, a decision the ageing profile informs. The variability buffer is sized from the variance of daily arrivals and of handling time and is inferred practice; a simulation of the day's arrivals and closures can replace it with a distribution of end-of-day age, and the simulation-based staffing methods developed for call centres transfer to this use. The planning unit is the shift or day because arrivals across the goal window are not stationary, and the staffing literature treats time-varying demand as its own problem rather than a sequence of stationary intervals. The inputs, their source rows and the model version are recorded on the model's lineage card, LN-004 (Data Lineage Card for Planning Models).

One caution on the handling-time input is established: where pace is estimated from history, the history is censored by work availability and shaped by the incentive to slow down when work is scarce, so throughput history can understate capacity. Handling time measured per touch is less exposed than productive time divided by items closed.

Why a goal in hours makes Erlang C the wrong instrument

Erlang C assumes Poisson arrivals, exponential service, identical agents, patient callers and a stationary arrival rate. For a deferred queue it fails four ways, and the first is arithmetic.

The target falls outside the formula's useful range. Under Erlang C the probability that an arriving item waits longer than t is C(c, a) · exp(−(c − a) t ⁄ s), where a is the offered load in Erlangs, c the agents and s the mean handling time. Take 120 items an hour at 10 minutes each, so a = 20. With 21 agents the probability of waiting more than 20 seconds is 0.74 [C], the familiar voice result; the probability of waiting more than 8 hours is about 10⁻²¹ [C]. Any hours-scale target is met by one agent above the offered load (the implication is inferred; the formula is established). The instrument collapses to staff to workload plus a hair, says nothing about day-to-day variation or the backlog, and reports a service level of effectively 100 percent for a queue that may be ageing badly. The check is computed, not published, and is shown so a reader can repeat it.

Arrivals are not stationary across the goal window. A goal of 24 hours spans the daily cycle; the formula assumes one rate.

Service is not first-come-first-served by whichever agent frees. Email is batched, sorted, pended and ordered by agent choice. This failure is inferred from practice.

Pace depends on queue length. The censoring and incentive effects above mean the service-time input is not the fixed rate the formula wants.

A queueing model keeps a place at the short end. Where the goal is tens of minutes to about two hours, worked from a live queue by dedicated agents, a delay model is defensible, with Erlang-A or a simulation preferred to Erlang C. Where the goal is hours to days, the workload model applies. Where the email agents also answer calls, the two-class models on Multichannel Capacity Model Assembly apply, and the reserve rule, not a share of an available state, is the control. The boundaries are inferred from the established components.

Worked example

The numbers are synthetic and graded [E]; everything computed from them is [C] on [E] inputs. A team works an email queue with a goal of closing items within 24 hours of arrival. One weekday: 420 items arrive [E]; handling time from touch-level capture averages 9.5 minutes per item [E]; 60 items are open at the start of the day [E]; each agent contributes 5.2 productive hours to the channel [E], being 8.0 scheduled hours less 2.0 hours of shrinkage less 0.8 hours of voice overflow in-work time.

Arrival workload is 420 × 9.5 ÷ 60 = 66.5 hours [C]. Clearing the opening backlog adds 60 × 9.5 ÷ 60 = 9.5 hours [C], total 76.0 hours [C], which on its own would need 76.0 ÷ 5.2 = 14.6, so 15 agents [C]. Daily arrivals have a standard deviation of 50 items [E], so a one-standard-deviation buffer is 50 × 9.5 ÷ 60 = 7.9 hours [C], and the requirement with the buffer is 76.0 + 7.9 = 83.9 hours ÷ 5.2 = 16.1, so 17 agents [C]. The sensitivity runs the other way too: with 14 agents the day's capacity is 14 × 5.2 × 60 ÷ 9.5 = 459 items [C]; closures are bounded there, so the end-of-day backlog is 60 + 420 − 459 = 21 items [C]. The ageing profile, not a Little's Law mean, gives the age of the residual 21; under arrival-order service they are the day's last arrivals.

The same day through Erlang C: 52.5 items an hour at 9.5 minutes is a = 8.3 Erlangs; with 9 on-queue agents the probability of waiting more than 8 hours is effectively zero [C]. The instrument answers nine agents, which is the 66.5 workload hours divided by the 8.0 hours it silently assumes each on-queue agent gives, and it has no term for the 60-item backlog, for the shrinkage that leaves 5.2 productive hours, or for a two-standard-deviation day of 520 arrivals.

Maturity Model Position

Four scales on this wiki use the word level; the launch page states which is which. On the WFM Labs Maturity Model™ a function is at Level 2 for this channel when it counts items closed, holds a handling time per item from any instrument with its grade stated, and sizes deferred work on workload hours rather than on a telephony formula. Level 3 adds touch-level capture, a published ageing profile and the backlog rolled forward daily, the precondition for the automation layer to reprioritize work by age. At Level 4 the ageing profile and the reserve rule are read by routing, so deferred work is released to blended agents against a published threshold.

See Also

• Workforce Data Definitions Framework — the hub this model belongs to
• Agent Time Accounting Model — where productive hours per agent are read from
• Email Handle Time Measurement — the instrument for the handling-time input
• Workload Units and the Roll-Up to FTE — the ladder the two units climb
• Multichannel Capacity Model Assembly — where the email requirement meets the voice requirement
• Reconciliation Tests for Time Accounting — test T-05, item count against time
• Back Office and Knowledge Worker Workforce Management — the planning discipline for deferred work
• Little's Law Applied to WFM — the stock-to-delay relation and its scope
• Erlang C — the synchronous instrument and its assumptions
• Multi-Channel and Blended Operations — the operating choices around blending