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Cellular Digital Packet Data: Channel Availability

This article discusses modeling issues and presents a M/M/c/c model for analyzing the availability of idle AMPS air time for CDPD. It also explores CDPD essentials such as re-sniffing, forced hop, planned hop, blackout periods, and brownout periods.

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Cellular Digital Packet Data: Channel Availability

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  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 Prof. Huei-Wen Ferng

  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 Prof. Huei-Wen Ferng

  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. Prof. Huei-Wen Ferng

  5. M/M/c/c model A. System Model B. State-transition-rate diagram Formula: Prof. Huei-Wen Ferng

  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 • 3. denote the offered AMPS call load in the sector (cell) • 4. The number of channels in the sector is c Prof. Huei-Wen Ferng

  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 Prof. Huei-Wen Ferng

  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 Prof. Huei-Wen Ferng

  9. How much idle AMPS air time is there? (cont’d) Prof. Huei-Wen Ferng

  10. How much idle AMPS air time is there? (cont’d) Prof. Huei-Wen Ferng

  11. CDPD essentials Prof. Huei-Wen Ferng

  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 Prof. Huei-Wen Ferng

  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 Prof. Huei-Wen Ferng

  14. CDPD essentials (cont’d) Prof. Huei-Wen Ferng

  15. Prof. Huei-Wen Ferng

  16. 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 Prof. Huei-Wen Ferng

  17. How efficiently does CDPDuse 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 Prof. Huei-Wen Ferng

  18. How efficiently does CDPDuse 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 Prof. Huei-Wen Ferng

  19. How efficiently does CDPDuse idle AMPS capacity? (cont’d) Prof. Huei-Wen Ferng

  20. How efficiently does CDPDuse idle AMPS capacity? (cont’d) Prof. Huei-Wen Ferng

  21. How efficiently does CDPDuse idle AMPS capacity? (cont’d) Prof. Huei-Wen Ferng

  22. How efficiently does CDPDuse idle AMPS capacity? (cont’d) Prof. Huei-Wen Ferng

  23. CDPD brownout periods Brownout periods: when there are not enough idle AMPS channels to accommodate all k CDPD channel streams Prof. Huei-Wen Ferng

  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 Prof. Huei-Wen Ferng

  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 Prof. Huei-Wen Ferng

  26. CDPD brownout periods (cont’d) Prof. Huei-Wen Ferng

  27. CDPD brownout periods (cont’d) Prof. Huei-Wen Ferng

  28. CDPD brownout periods (cont’d) Prof. Huei-Wen Ferng

  29. CDPD brownout periods (cont’d) Prof. Huei-Wen Ferng

  30. CDPD brownout periods (cont’d) Prof. Huei-Wen Ferng

  31. CDPD brownout periods (cont’d) Prof. Huei-Wen Ferng

  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. Prof. Huei-Wen Ferng

  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. Prof. Huei-Wen Ferng

  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. Prof. Huei-Wen Ferng

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