$.$ Consider a simple call center that works for seven days a week and $24$ hours a day. The call center works in $2$

shifts. The first shift starts at $08$:$00$ and ends in $20$:$00,$ employing $3$ identical call center agents. The second shift

starts at $20$:$00$ and ends in $08$:$00,$ employing $2$ identical call center agents. In the end of the first shift, if the third

agent is busy, s$/$he does not end his$/$her shift until that task is complete. However, s$/$he does not compensate this

extra work, and tomorrow, s$/$he starts his$/$her shift at the regular time at $08$:$00.$

Through out the day, the inter$-$arrival times of the calls arriving to the center $($and the arrival of the first caller$)$

follow exponential distribution with an average of $5$ minutes. The callers are calling according to a Poisson process

with a rate $\backslash$lambda $=12$ calls per hour. When a caller calls, s$/$he waits until an agent becomes idle, then the service

starts. A caller can be any of the three types of callers:

$$ Type I Caller: $20\%$ of the callers are Type I callers. The service duration of type I callers is normally

distributed with an average of $12$ minutes and standard deviation of $1\mathrm{.}75$ minutes.

$$ Type II Caller: $42\%$ of the callers are Type II callers. The service duration in minutes of type II callers is

Erlang distributed with shape parameter k $=4$ and scale parameter $($exponential mean$)2\mathrm{.}5.$

$$ Type III Caller: $38\%$ of the callers are Type III callers. The service duration of type III callers is deterministic

with fixed period of $12\mathrm{.}25$ minutes.. Consider a simple call center that works for seven days a week and $24$ hours a day. The call center works in $2$

shifts. The first shift starts at $08$:$00$ and ends in $20$:$00,$ employing $3$ identical call center agents. The second shift

starts at $20$:$00$ and ends in $08$:$00,$ employing $2$ identical call center agents. In the end of the first shift, if the third

agent is busy, s$/$he does not end his$/$her shift until that task is complete. However, s$/$he does not compensate this

extra work, and tomorrow, s$/$he starts his$/$her shift at the regular time at $08$:$00.$

Through out the day, the inter$-$arrival times of the calls arriving to the center $($and the arrival of the first caller$)$

follow exponential distribution with an average of $5$ minutes. The callers are calling according to a Poisson process

with a rate $\backslash$lambda $=12$ calls per hour. When a caller calls, s$/$he waits until an agent becomes idle, then the service

starts. A caller can be any of the three types of callers:

$$ Type I Caller: $20\%$ of the callers are Type I callers. The service duration of type I callers is normally

distributed with an average of $12$ minutes and standard deviation of $1\mathrm{.}75$ minutes.

$$ Type II Caller: $42\%$ of the callers are Type II callers. The service duration in minutes of type II callers is

Erlang distributed with shape parameter k $=4$ and scale parameter $($exponential mean$)2\mathrm{.}5.$

$$ Type III Caller: $38\%$ of the callers are Type III callers. The service duration of type III callers is deterministic

with fixed period of $12\mathrm{.}25$ minutes.