Telephony Example 1

Telephony Systems: Modular Supervisory Control




• Description
  
  
• This telephone system consists of three subscribers, each connected to the network through a different switch, as shown in the figure above; the network will be controlled by decentralized supervisors implemented at individual switches.



• System Models
  
  
• Our model of the uncontrolled network is built up of three components, each of which can be thought of as representing the event sequences that can be set in motion by a single subscriber. A typical such component is the generator of the figure below, representing the actions of subscriber i.

• While the automaton is in state 0, the initial state, subscriber i can go off-hook (i.e. lift his telephone handset off the hook-switch) as signified by the event off-h_i; he can then go on-hook immediately (on-h_i) or dial a number, thereby requesting the establishment of a connection across the network (req_ij). This request can be answered with the establishment of a connection (con_ij) or through the transmission of a busy tone or other signal indicating that no connection is forthcoming (no-con_ij). In order to define a notion of blocking, we add to our model a "marked language": the set of all event strings labelling paths through this transition structure that both begin and end in state 0. The entire network, in the absence of control, is modelled as the synchronous product of three generators of the form of that of the above figure.



• As our controllers will be designed to be implemented at the level of individual switches, they will not observe all of the events generated by the three system components. We therefore adopt the appraoch of decentralized supervisory control, specifying a local alphabet of event symbols for each controller; the local alphabet for controllers implemented at subscriber i's switch is given in the table below.



• Feature Interaction
  
  
• Consider that our system has an "originating call screening" (OCS) service, which allows a subscriber to prevent the making of calls from his own equipment to any numbers on a prespecified list. Suppose that subscriber i wishes to prevent calls to subscriber k. We may construct an automaton that recognizes the appropriate "legal language" by taking a copy of the local model and deleting the event con_ik, which represents the establishment of the forbidden call. The supremal controllable sublangauge of this legal language corresponds to the control policy that simply disables the out-going request req_ik that can lead to the connection con_ik. This is clearly the minimally restrictive control strategy that satisfies the specification.



• We now wish to extend our model to allow for a call forwarding feature. As call fowarding can convert a pending call to a subscriber j into a pending call to some subscriber k, a natural way to extend our model of subscriber i would appear to be to add events fwd_xyz to our model as shown in the figure below. Thinking of the forwarding of a call from j to k (e.g. fwd_ijk) as taking place at j's switch, it also seems natural that fwd_ijk should be uncontrollable at switch i.

• The addition of these forwarding events, however, interferes with the OCS service. If we define our OCS specification language as before, by simply deleting con_ik from a copy of the local system model, then we find that the supremal controllable sublanguage corresponds to the control strategy that disables not only req_ik but also req_ij, and fwd_iij and fwd_iik. As forwarding can convert a pending call to j to a pending call to k, and as forwarding is uncontrollable by switch i, the OCS specification can only be enforced by preventing all outgoing calls.



• It is clearly unacceptable that the subscriber be prevented from making outgoing calls. We can resolve this issue by dividing the forwarding event into two stages, as in the figure below. Here, an event fwd_ijk now represents only the initiation of the forwarding; the event must then be followed by either an ordinary request req_ik to complete the forwarding or by a no-con_ii to advise subscriber i that his call has been aborted. The second component in the figure models this restraint. In either case, this second step would be under the control of i's switch. The new model of subscriber i's action is the synchronous product of these two components. We therefore resolve the interaction between OCS and call forwarding by creating a supervisor that simply disables req_ik.

• For more information on this example:
• Thistle, J. G., Malhame, R. P., Hoang, H.-H., and Lafortune, S. "Feature interaction modelling, detection and resolution: A supervisory control approach." Feature Interactions in Telecommunications and Distributed Systems IV, 93-107. IOS Press, 1997.
• Chen, Y.L., Lafortune, S., and Lin, F., "Resolving Feature Interactions Using Modular Supervisory Control with Priorities," Feature Interactions in Telecommunications and Distributed Systems IV, 108-122. IOS Press, 1997.