THE EXPECTED REMAINING SERVICE TIME IN A SINGLE-SERVER QUEUE

FOR THE G/G/1 QUEUEING SYSTEM, LET (P//N),N = 0,1,2,. . . ,AND (R//N), N = 0, 1,2,. . . BE THE LIMITING PROBABILITY DISTRIBUTIONS OF THE NUMBER OF CUSTOMERS IN THE SYSTEM, WHEN THE SYSTEM IS CONSIDERED ″ AT ANY TIME ″ AND WHEN IT IS CONSIDERED AT ARRIVAL EPOCHS RESPECTIVELY. ALSO LET B//N(N = 1,2,. . . ) BE THE MEAN REMAINING DURATION OF THE SERVICE IN PROGRESS AT THE EPOCH OF AN ARRIVAL WHICH FINDS N CUSTOMERS IN THE SYSTEM. IN THIS WORK A RELATION BETWEEN THE SEQUENCES (P//N), (R//N) AND (B//N) IS GIVEN AND IT IS USED TO PROVIDE ALTERNATIVE DERIVATIONS FOR TWO WELL-KNOWN RESULTS IN THE THEORY OF QUEUES.