At a node in a computer network, a message packet requires X time units to be transmitted over a link, where X $=$ geom$($p$),0<$ p $<1.$ A single new message packet arrives in a time unit with probability q$,0<$ q $<1$; and no message packet arrives with probability $1$q$.$ Such new message arrivals occur in an independent and identical manner. Let Y be the number of new message packet arrivals during the transmission of a single message packet.