This study is directed to the problem of the quantitative determination of the number of additional personnel required in an organization for servicing unscheduled priority tasks without delaying the completion of scheduled tasks. The manager of an organization which has been enlarged in order to respond adequately to the random arrival of priority requests may face criticism if the organization appears to be "overstaffed" during periods when only "routine" service requirements must be met. An audit team oriented toward accounting-type data may be reluctant to accept a manager's justification of his organization's size if the justification is based primarily on nonquantitative arguments.