Cellular digital packet data (CDPD) provides a sleep-mode operation for power conservation in mobile end systems (M-ESs). We perform a theoretical analysis of sleep-mode operation for CDPD. Sleep-mode operation is modeled as an M-x/G/1/L queueing system with an attention span and multiple vacations with an exceptional first,vacation. The steady-state probabilities of the queueing system, the frame. loss probability, the expected frame waiting time, and the percentage of time in the sleep period are derived. Sleep-mode performance is evaluated for varying packet arrival rate, buffer length, and timers' values using the queueing model. Sleep mode in an M-ES occurs when the packet arrival rate for the M-ES is low. When the M-ES is in sleep mode, the expected frame waiting time depends on T204 value. To keep the frame loss probability low for M-ES in sleep mode, the mobile data intermediate system buffer should be sufficiently large. Sleep mode can efficiently reduce power consumption by selecting a low value for timer T203 and a high value for timer T204.