that is t u2514 u03b4 u03c4 u2518 where t is the id of the last selected telephone knowing that the queried telephones can have an id that spans the range from 1 to t u2514 u03b4 u03c4 u2518 a binary search can be performed to find the telephone with the largest id it can be easily shown that this binary search will require at most u250c log q u2510 query message response iterations where u250c u2510 symbol represents rounding up to the next integer for example u250c 3 1415 u2510 4 advantageously u03c4 is selected to be long enough so that u2514 a u03c4 u2518 does not change during the binary search choosing a large value of u03c4 which means choosing a coarse granularity creates the possibility that two or more telephones that cease being idle within u03c4 sec of each other will carry the same id eventually these telephones will be the telephones with the longest idle time a possibility exists therefore that a telephone with the longest actual idle time is not selected in favor of a telephone with a slightly shorter idle time that is within u03c4 sec of the telephone with the longest idle time in the above example that can only generate a 1 sec discrepancy which has no material effect since the next polling times will definitely select from among those telephones that shared the same id the binary search to find the telephone with the largest id can be by means of a program executed by switching apparatus 200 as described below where x designates the condition that a telephone exists with an id.