Optimizing YM Chat Conversation for Two.

Mutually Available Time Model for 2 – person chat cited in support of
Loophole Claim in the Urge to Bond Argument.
Obliv[+]ion. YM proceedings 2005. Vol. XXV No. 8

Let, for two chatters A and B:
tA = time available for A to talk/chat
tB = time available for B to talk/chat
tA(bar) = time available to A but same timeslot not available to B
tB(bar) = time available to B but same timeslot not available to A

then, in the nominal case,

mutual time available, TM = Sigma(i = 1 to n [tAi + tBi - tA(bar)i - tB(bar)i]/2 … Eqn. 1

where i is an integer representing an instant of time slot available

Let Deltat represent the time interval spent in servicing chat requests from a third-party
chatter. Then, mutual time available to chat (Eqn.1)will be modified as follows:

TM = Sigma ( i = 1 to n [tAi + tBi - tA(bar)i - tB(bar)i]/2 - (j = Sigma 1 to n Deltatj - P* tswitch ** (j+1) ... Eqn. 2.

Where j is the number of additional third-party chatters, and tswitch is the time required to switch context from chat window to chat window, while P represents the probability, with a maximum limiting value of Unity, that all j third-party chatters are online and wanting to talk to either of A or B at the same time.

It is clear from the above that for any given P, as j increases linearly it decreases the mutually available time T in a linear fashion, but the second term reduces the mutually available time at an exponential rate as the number of third-party chatters increases.

So if 1/ TM is a scalar representing the emotional separation between A and B, then 1/ TM increases as the number of simultaneous third-party chatters increases.

The obvious management problem here is to optimize j such that the objective of bonding with as many third-party chatters is met, without exceeding the maximum separation tolerance between A and B.
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The “loophole” in the Bonding argument (see The ‘Urge to Bond’ as Applied to the Defense of Chat Latency Caused by Multiple Windows, author reference withheld by request, YM proceedings 2005. Vol. XXV No. 7), therefore, is that j cannot be increased without limit without compromising either one of the two objectives.

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