Trace a Queue with Explicit Arrivals and Service
Add arrivals to the starting backlog,then subtract completed service under the stated order.
About 22 minutes, plus any extended practice
Supplied materials
- Paper and pencil; answers may also be spoken or typed.
- All cases, labels, numbers and rules are supplied on this page. No real account, private information or purchase is needed.
Learn the idea
A queue model can count backlog after arrivals and completed service. Our exercise begins with a stated nonnegative backlog,adds new tasks,then completes a stated number that does not exceed the available tasks. These counts do not model retries,priority or variable service times.
Add arrivals to the starting backlog,then subtract completed service under the stated order. Do not subtract more completed work than the model makes available.
Use this supplied case: One paper tick: backlog 2; arrivals 3; then 1 tasks completed. New backlog? The task is to connect the given information to the computing idea. Write a short evidence trail so another learner can reproduce your choice. The simplified case describes the stated model, not every real system.
- Represent the supplied worked case with a labeled drawing, table or short trace.
- Add arrivals to the starting backlog,then subtract completed service under the stated order.
- Explain why the worked answer fits and why one alternative does not.
- Try the new check and practice cases; revisit the stated rule if your evidence does not match.
See the method in action
One paper tick: backlog 2; arrivals 3; then 1 tasks completed. New backlog? The supported answer is 4 tasks. Applying the stated rule gives 4 tasks. Add arrivals to the starting backlog, then subtract completed service under the stated order. Do not subtract more completed work than the model makes available. A queue model can count backlog after arrivals and completed service. Calculation: ((2+3)-1) = 4.
Check your reasoning
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Helpful tips
- Add arrivals to the starting backlog,then subtract completed service under the stated order.
- Do not subtract more completed work than the model makes available.
See the answer and explanation
3 tasks
Using the supplied inputs: ((3+2)-2) = 3. Add arrivals to the starting backlog,then subtract completed service under the stated order. Do not subtract more completed work than the model makes available.
Take it further
New tick backlog 3, arrivals 4, completions 2 gives 5 waiting. A rule capping service at available work would be needed for an excessive completion request.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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Check the subject sources
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