1. Cellular Digital Packet Data: Channel Availability
From: IEEE Trans. Veh. Technol.,
vol. 46, pp , 1997
Author: K. C. Budka

2. Outline Modeling issues M/M/c/c model
How much idle AMPS air time is there?
CDPD essentials
How efficiently does CDPD use idle AMPS capacity?
CDPD brownout periods
Summary
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3. Modeling issues Input process
In the cellular system, voice users are frequently modeled by a Poisson process
What’s Poisson process
Its inter-arrival time distribution is exponential
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4. Modeling issues (cont’d)
System model
System capacity is the number of channels, say c fixed channels
Each call duration is modeled by an exponential distribution with mean
The resultant model can be captured by the queueing model M/M/c/c.
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5. M/M/c/c model Formula: A. System Model
B. State-transition-rate diagram
Formula:
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6. How much idle AMPS air time is there?
Assumption:
AMPS call attempts and handoffs in a sector are
generated in accordance with a Poisson process of rate
2. AMPS call holding time is generally distributed with mean
denote the offered AMPS call load in the sector (cell)
4. The number of channels in the sector is c
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7. How much idle AMPS air time is there? (cont’d)
B (c , a) denotes the call blocking probability of load a
denotes the fraction of time each AMPS channel in a sector is occupied
by an AMPS call
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8. How much idle AMPS air time is there? (cont’d)
denotes the average length of time when each AMPS channel
in the sector is idle
and hence
denotes the average number of AMPS channels in the sector
that is not occupied by an AMPS call
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9. How much idle AMPS air time is there? (cont’d)
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10. How much idle AMPS air time is there? (cont’d)
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11. CDPD essentials
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12. CDPD essentials (cont’d)
Re –sniffing:
to passively detect whether AMPS channels are idle or
busy carrying an AMPS call without direct communication
with the AMPS network.
Forced hop:
if an AMPS call suddenly starts using the AMPS channel
a CDPD channel stream occupies, the affected CDPD
channel stream quickly ceases transmission
(in less than 40 ms) and hops to a new idle AMPS channel.
Planned hop:
a CDPD channel stream may be moved to a different
AMPS channel in a planned hop manner when
preemption by an AMPS call is imminent
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13. CDPD essentials (cont’d)
Blackout period:
if CDPD channel stream hops and no idle AMPS channel
can be found, it enters into this period during which no data
can be transmitted or received over the CDPD channel
Active period:
the system is able to assign the CDPD channel to an
idle AMPS
Mobile data base station (MDBS):
is responsible for finding idle AMPS channels and
assigning CDPD channel streams to them
Mobile data-intermediate system (MDIS)
the CDPD switching element responsible for
managing mobility
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14. CDPD essentials (cont’d)
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15. 2019/1/2
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16. How efficiently does CDPD use idle AMPS capacity?
denotes the probability that i AMPS channels are occupied by AMPS calls
denote the average rate at which CDPD channel are blacked out
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17. How efficiently does CDPD use idle AMPS capacity? (cont’d)
denotes the average number of CDPD channel streams that are blacked out
at any given time
denotes the average length of time a CDPD channel stream is blacked out
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18. How efficiently does CDPD use idle AMPS capacity? (cont’d)
denotes the mean length of time a CDPD channel stream is active
The fraction of time a CDPD channel stream is active equals
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19. How efficiently does CDPD use idle AMPS capacity? (cont’d)
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20. How efficiently does CDPD use idle AMPS capacity? (cont’d)
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21. How efficiently does CDPD use idle AMPS capacity? (cont’d)
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22. How efficiently does CDPD use idle AMPS capacity? (cont’d)
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23. CDPD brownout periods
Brownout periods: when there are not enough idle AMPS channels to
accommodate all k CDPD channel streams
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24. CDPD brownout periods (cont’d)
Let denote the probability density function of the length of time n
or more AMPS channels in sector are occupied with AMPS calls. Let
denote the Laplace transform ([2] derived the following formulas).
Recursive expression for the mean length
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25. CDPD brownout periods (cont’d)
Let denote, respectively, the probability density function and its Laplace transform of the length of time fewer than n AMPS channels are occupied with AMPS calls.
Recursive expression for the mean length
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26. CDPD brownout periods (cont’d)
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27. CDPD brownout periods (cont’d)
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28. CDPD brownout periods (cont’d)
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29. CDPD brownout periods (cont’d)
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30. CDPD brownout periods (cont’d)
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31. CDPD brownout periods (cont’d)
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32. Summary
The total amount of spare capacity available to CDPD in an AMPS sector can be easily calculated from the offered call load and the number of AMPS channels.
The amount of spare AMPS capacity available to CDPD is independent of the mean AMPS channel holding time.
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33. Summary (cont’d)
As the AMPS call load in an AMPS sector increases, the amount of capacity available to CDPD decreases. Also, the length of time each AMPS channel is idle decreases, causing CDPD channel streams to hop more frequently.
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34. Summary (cont’d)
Increasing the number of CDPD channel streams equipped in an AMPS sector increases the amount of data that can be carried by CDPD. Results obtained in this paper can be used to quantify the CDPD data carrying capacity of an AMPS sector equipped with an arbitrary number of CDPD channel streams.
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