Round Trip Time (RTT) Analysis in
Mobile-Cloud-Collar Communication
Pedro Soares
October 2024
1 Mathematical Simulation Analysis
1.1 Parameters
• Mobile Send Rate (Rm): The interval at which the mobile device sends a
message.
• Tolerance (T ): The time buffer to handle processing delays and variability.
• Processing Delay (Dp): The combined delay between message generation
and evaluation, both on the cloud and collar side.
• Future Timestamp (tfuture): Indicates the future time when the RTT will
expire unless refreshed by another message.
1.2 Example 1: Mobile send rate 5 seconds
Given:
• Mobile Send Rate (Rm): 5 s
• Tolerance (T ): 15 s
• Processing Delay (Dp): 5 s
• Future Timestamp (tfuture): 60 s from the current time
1.2.1 Worst-case Scenario Analysis
Consider the following sequence of events:
1. User triggers an action that will send a message from mobile when RTT
timestamp will expire in 18 s.
2. Cloud evaluates sending the message when RTT timestamp will expire in
15.5 s (after 2.5 s of processing).
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3. Since 15.5 s ≥ T (15 s), the message is not sent, and the mobile timer
resets to 5 s.
4. After 5 s, cloud receives a new message when RTT timestamp will expire
in 13 s.
5. Cloud evaluates this message when RTT timestamp will expire in 10.5 s
(after 2.5 s of processing).
6. Since 10.5 s ≤ T (15 s), a message is sent to the collar.
7. Message reaches the collar when RTT timestamp will expire in 8 s, refresh-
ing the RTT timestamp.
In this case, the maximum interval at which the collar will receive messages
is 40 s (tfuture − T = 60 − 15 − 5 40).
1.3 Example 2: Mobile send rate 45 seconds
Given:
• Mobile Send Rate (Rm): 45 s
• Tolerance (T ): 55 s
• Processing Delay (Dp): 5 s
• Future Timestamp (tfuture): 100 s from the current time
1.3.1 Worst-case Scenario Analysis
Consider the following sequence of events:
1. User triggers an action that will send a message from mobile when RTT
timestamp will expire in 58 s.
2. Cloud evaluates sending the message when RTT timestamp will expire in
55.5 s (after 2.5 s of processing).
3. Since 55.5 s ≥ T (55 s), the message is not sent, and the mobile timer
resets to 45 s.
4. After 45 s, cloud receives a new message when RTT timestamp will expire
in 13 s.
5. Cloud evaluates this message when RTT timestamp will expire in 10.5 s
(after 2.5 s of processing).
6. Since 10.5 s ≤ T (55 s), a message is sent to the collar.
7. Message reaches the collar when RTT timestamp will expire in 8 s, refresh-
ing the RTT timestamp.
In this case, the maximum interval at which the collar will receive messages
is 52 s (tfuture − T = 100 − 55 − 5 40).
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1.4 Example 3: Mobile send rate 45 seconds but collar
receives at max 1 message every 60 seconds
Given:
• Mobile Send Rate (Rm): 45 s
• Tolerance (T ): 55 s
• Processing Delay (Dp): 5 s
• Future Timestamp (tfuture): 120 s from the current time
1.4.1 Worst-case Scenario Analysis
Consider the following sequence of events:
1. User triggers an action that will send a message from mobile when RTT
timestamp will expire in 58 s.
2. Cloud evaluates sending the message when RTT timestamp will expire in
55.5 s (after 2.5 s of processing).
3. Since 55.5 s ≥ T (55 s), the message is not sent, and the mobile timer
resets to 45 s.
4. After 45 s, cloud receives a new message when RTT timestamp will expire
in 13 s.
5. Cloud evaluates this message when RTT timestamp will expire in 10.5 s
(after 2.5 s of processing).
6. Since 10.5 s ≤ T (55 s), a message is sent to the collar.
7. Message reaches the collar when RTT timestamp will expire in 8 s, refresh-
ing the RTT timestamp.
In this case, the maximum interval at which the collar will receive messages
is 60 s (tfuture − T = 120 − 55 − 5 60).