Loo-Q: the example in full

Here is our worked example of the Loo-Q system in all its glory!

For simplicity we consider a system of just three seats – A, B and C. The table shows the global history, with a description of the event and the status of the local queues at each time.

The spacetime diagram of the system is on the right, showing the processes for seats A, B and C as vertical lines with time increasing as you move up. Messages sent between processes are shown as dashed lines. An event is shown as green if that seat's Loo-Q button is green.

Time	Event	Queue A	Queue B	Queue C
0.1	Start time for A
0.2	Start time for B
0.3	Start time for C
1.1	A: Rule 1 Sends message "1.1: A needs loo" to B and C	1.1 A needs loo
1.2	B: Rule 2 Receives message "1.1: A needs loo" Sends message "1.2: received" to A	1.1 A needs loo	1.1 A needs loo
1.3	C: Rule 2 Receives message "1.1: A needs loo" Sends message "1.3: received" to A	1.1 A needs loo	1.1 A needs loo	1.1 A needs loo
2.1	A: Rule 4 First in queue but hasn't received messages from B & C after 1.1	1.1 A needs loo	1.1 A needs loo	1.1 A needs loo
2.2	B: Rule 1 Sends message "2.2: B needs loo" to A and C	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo	1.1 A needs loo
2.3	C: Rule 1 Sends message "2.3: C needs loo" to A and B	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo	1.1 A needs loo 2.3: C needs loo
3.1	A: Rule 6 Receives message "1.2: received"	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo	1.1 A needs loo 2.3: C needs loo
3.2	B: Rule 2 Receives message "2.3: C needs loo" Sends message "3.2: received" to C	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.3: C needs loo
3.3	C: Rule 2 Receives message "2.2: B needs loo" Sends message "3.3: received" to B	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
4.1	A: Rule 6 Receives message "1.3: received"	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
4.2	B: Rule 6 Receives message "3.3: received"	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
4.3	C: Rule 6 Receives message "3.2: received"	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
5.1	A: Rule 4 First in queue and have received messages from B and C after 1.1	1.1 A needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
6.1	A: Rule 2 Receives message "2.2: B needs loo" Sends message "6.1: received" to B	1.1 A needs loo 2.2: B needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
6.2	B: Rule 6 Receives message "6.1: received"	1.1 A needs loo 2.2: B needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
7.1	A: Rule 4 Sends message "7.1: A has finished" to B and C	2.2: B needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
7.2	B: Rule 5 Receives "7.1: A has finished"	2.2: B needs loo	2.2: B needs loo 2.3: C needs loo	1.1 A needs loo 2.2: B needs loo 2.3: C needs loo
7.3	C: Rule 5 Receives "7.1: A has finished"	2.2: B needs loo	2.2: B needs loo 2.3: C needs loo	2.2: B needs loo 2.3: C needs loo
8.1	A: Rule 2 Receives message "2.3: C needs loo" Sends message "8.1: received" to C	2.2: B needs loo 2.3: C needs loo	2.2: B needs loo 2.3: C needs loo	2.2: B needs loo 2.3: C needs loo
8.2	B: Rule 4 First in queue and have received messages from A and C after 2.2	2.2: B needs loo 2.3: C needs loo	2.2: B needs loo 2.3: C needs loo	2.2: B needs loo 2.3: C needs loo
8.3	CL Rule 6 Receives message "8.1: received"	2.2: B needs loo 2.3: C needs loo	2.2: B needs loo 2.3: C needs loo	2.2: B needs loo 2.3: C needs loo
9.2	B: Rule 4 Sends message "9.2: B has finished" to A and C	2.2: B needs loo 2.3: C needs loo	2.3: C needs loo	2.2: B needs loo 2.3: C needs loo
9.3	C: Rule 5 Receives "9.2: B has finished"	2.2: B needs loo 2.3: C needs loo	2.3: C needs loo	2.3: C needs loo
10.1	A: Rule 5 Receives "9.2: B has finished"	2.3: C needs loo	2.3: C needs loo	2.3: C needs loo
10.3	C: Rule 4 First in queue and have received messages from A and B after 2.3	2.3: C needs loo	2.3: C needs loo	2.3: C needs loo

Back to main article