Staggered extended sleep cycles, comprising on and off sleep durations, in wireless devices

A system comprising:

• a wireless device comprising at least one hardware processor and one or more software modules that, when executed by the at least one hardware processor of the wireless device,
• synchronize parameters, defining an extended-sleep cycle, with a remote system, and,
• in an idle mode of the wireless device, operate according to an extended-sleep cycle, comprising an extended-sleep-ON duration an extended-sleep-OFF duration, by, over a plurality of extended-sleep cycles,
• during the extended-sleep-ON duration of the extended-sleep cycle, monitoring paging occasions, transmitted by a wireless communication network, and
• during the extended-sleep-OFF duration of the extended-sleep cycle, not monitoring the paging occasions;
• and
• a remote system comprising at least one hardware processor and one or more software modules that, when executed by the at least one hardware processor of the remote system,
• receive a message to be transmitted to the wireless device,
• based on the synchronized parameters, determine a transmission time at which to transmit the message over the wireless communication network such that the message will be received within the extended-sleep-ON duration of an extended-sleep cycle at the wireless device,
• queue the message until the transmission time,
• at the transmission time, transmit the message over the wireless communication network to the wireless device, and
• smooth an amount of messages trafficked between the remote system and a plurality of wireless devices, including the wireless device, by defining the synchronized parameters for each of the plurality of wireless devices such that the extended-sleep cycle at each wireless device is staggered with respect to the extended-sleep cycle of at least one other one of the plurality of wireless devices;
• wherein, for each of the plurality of wireless devices, a timing of the extended-sleep cycle i of that wireless device is defined by:
• TB(i)=T0+(exsSleepCycleLength*PCL*i)+(S*PCL),
• wherein T0 is an offset of a universal time standard,
• wherein exsSleepCycleLength is a duration of the extended-sleep cycle,
• wherein PCL is a length of a paging cycle, and
• wherein S is a parameter that is specific to the wireless device;
• and
• wherein, for each of the plurality of wireless devices, S is defined by:
• S=IMSI modulo exsSleepCycleLength,
• wherein IMSI is an international mobile subscriber identity of the wireless device.