Cellular Digital Packet Data: Channel Availability

1
Cellular Digital Packet Data Channel
Availability

• From IEEE Trans. Veh. Technol.,
• vol. 46, pp. 31-40, 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 CDPDuse idle AMPS capacity?
• CDPD brownout periods
• Summary

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Modeling issues

• Input process
• In the cellular system, voice users are
  frequently modeled by a Poisson process
• Whats Poisson process
• Its inter-arrival time distribution is
  exponential

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Modeling issues (contd)

• 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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M/M/c/c model

A. System Model
B. State-transition-rate diagram
Formula
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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
• 3. denote the offered AMPS call load
  in the sector (cell)
• 4. The number of channels in the sector is c

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How much idle AMPS air time is there? (contd)
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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How much idle AMPS air time is there? (contd)
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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How much idle AMPS air time is there? (contd)
10
How much idle AMPS air time is there? (contd)
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CDPD essentials
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CDPD essentials (contd)
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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CDPD essentials (contd)
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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CDPD essentials (contd)
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(No Transcript)
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How efficiently does CDPDuse 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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How efficiently does CDPDuse idle AMPS capacity?
(contd)
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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How efficiently does CDPDuse idle AMPS capacity?
(contd)
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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How efficiently does CDPDuse idle AMPS capacity?
(contd)
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How efficiently does CDPDuse idle AMPS capacity?
(contd)
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How efficiently does CDPDuse idle AMPS capacity?
(contd)
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How efficiently does CDPDuse idle AMPS capacity?
(contd)
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CDPD brownout periods
Brownout periods when there are not enough idle
AMPS channels to
accommodate all k CDPD channel streams
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CDPD brownout periods (contd)
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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CDPD brownout periods (contd)
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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CDPD brownout periods (contd)
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CDPD brownout periods (contd)
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CDPD brownout periods (contd)
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CDPD brownout periods (contd)
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CDPD brownout periods (contd)
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CDPD brownout periods (contd)
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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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Summary (contd)

• 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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Summary (contd)

• 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.