# On Distributed Communications Series

#### VI. Perishability Control

A communications network can deliver more traffic than a recipient can answer. We wish to prevent oscillation by feeding back processing status as a function of perishability.

First, we shall consider the number of parameters needed to specify the perishability of "messages" of various utilities transmitted in a communications network. Perishability and importance are not synonymous. Inasmuch as we pay for data transmission we assume that we must receive some utility when the message is correctly received by the recipient. The earlier the message arrives, the more useful it will be, as represented in Fig. 8. Such a message might be a telegraph request for a hotel reservation, transmitted while one is rushing out the door to catch an airplane. If the message arrives after the time requested for the reservation, it has a utility of zero. If the message arrives early enough to guarantee a room, then it has a relatively high utility. While we lack a good metric for communications utility, it is sufficient in this discussion to let it be equal to the quantity, 1-P

pb, where Ppb is the probability of sleeping on a park bench. (Perhaps the economist's term "disutility" would be more fitting--the price for which one would be willing to sleep on the park bench.) Only two parameters of specification were needed to provide a reasonable measure of the value of the communication as a function of time:

1. Peak value of utility at t 0 (Point A in Fig. 8);
2. Last time the message had any value (Point B).

A second message example, illustrated in Fig. 9, is "I am bringing a guest home for dinner tonight." Here, three parameters of specification would be useful:

1. Peak value of utility at t = 0 (Point A);
2. Last time the message had any value (Point B);
3. Last time the message had a high value of utility (Point C).
(Parameter C might correspond to the last time one's wife could drive over to the grocery store and pick up more beer for thirsty guests.)

Figure 10 shows the value of instantaneous utility for three different messages: a message to initiate a large long-term project; a message to reserve a hotel room; and a message saying, "Merry Christmas." Only three points are needed to approximate the shape of each of these curves. We may, for example, ask the three questions:

1. How "important" is the message?
2. When would we like the message delivered?
3. When is the latest time the message would be of any value?

While it is possible to think of examples that require more than three specification parameters to delineate the instantaneous utility curve, three will suffice for our purpose. If the communications network knows these few parameters for all traffic in the network, it will be able to perform a rather sophisticated control function. Consider the narrow-funnel-neck problem, where many communications links terminate at a single individual. A communications system may have a capability of delivering more messages which need to be processed than a single end individual can handle. In our future communications system we seek to automatically inform the sender not only that the end addressee is busy, but that he has a processing backlog of an expected value of K minutes.

If this predicted time is acceptable to the sender, he will do nothing. Otherwise, he could increase his precedence indicator and try again.