Automatic self-optimizing queue management system
A queue management system for e.g. supermarket checkouts uses counting devices located at checkouts and optimally entrances/exits in conjunction with P.O.S. information to produce a schedule of how many checkouts are needed to avoid queue length exceeding preset limits. The system includes a dynamic learning system which can optimise calculated schedules on the basis of historical data.
1. A method of operating a queuing system for users queuing to use a facility, the method comprising:
a) providing a plurality of said facilities that can be rendered operative or inoperative depending on the number required,
b) determining the number of users Q queuing to use the facility,
c) determining a desired number of users N queuing to use the facility,
d) determining a number Â, of users expected to arrive at the facility during a future timestep m,
e) determining the expected time W taken for each user to use the facility,
f) calculating by a processing system the required number S of operative facilities at time t using the ratio of the expected queue length and arrivals, to the rate of departure, such that the desired number of users N is maintained at time t+m, said ratio being given by
Q
1
+
A
^
N
+
m
W
^
,
and
g) rendering S number of facilities operative.
2. A method as claimed in claim 1 in which step (d) includes determining the number of users arriving at the facility or facilities between time t and time t+1 from the formula:
A =( Q t+1 −Q t )+ P
where the P is the number of users that complete a transaction at the facility between t and t+1.
3. A method as claimed in claim 1 in which the determination of  is based on values of A determined over previous time periods and extrapolated to predict expected arrivals.
4. A method as claimed in claim 1 in which step (e) includes determining the actual time taken for a user to use the facility from previous time periods, using the formula:
W
=
m
*
S
P
where P is the number of user that complete a transaction at the facility between t and t+m.
5. A method as claimed in claim 1 in which the determination of Ŵ is based on average values determined over previous time periods and extrapolated to predict expected time per user.
6. A method as in claim 1 in which variable values used to determine S are adaptable to short term variances.
7. An automatic queue management system for users queuing to use facilities, the system comprising:
a plurality of facilities that can be rendered operative or inoperative according to the need,
means for counting the number Q t of users queuing to use the facilities at the time t,
timer means for determining the length of time W taken for each user to use the facility, and
processing means for receiving data from said counting means and said timer means and calculating a required number S of operative facilities at time t using the ratio of the expected queue length and arrivals, to the rate of departure, such that the target queue length is maintained at the end of a timestep m, said ratio being given by:
Q
1
+
A
^
N
+
m
W
^
,
where N is a predetermined desired number of users queuing per facility;
 is the number of users expected to arrive at the facility or facilities during the next timestep m; and
Ŵ is the expected length of time for incoming users to take to use the facility.
8. A system as claimed in claim 7 in which the values of  and Ŵ are calculated using an artificial neural network, support vector machine, liner or non-linear model, Bayesian inference network, Markov model or supervised learning fitted model.
9. A system as claimed in claim 7 further comprising counting means for counting numbers of users entering and/or leaving a defined space.
10. A system as claimed in claim 9 in which data from the counting means is used in the calculation of Â.
11. A system as in claim 7 , wherein the system monitors its own performance, and feeds back an error signal as an input into the learning system.
12. A system as in claim 7 , wherein the system monitors its own performance, and feeds back an error signal to guide the choice of which of a number of learning methods to apply to best predict  and/or Ŵ.