164 IEEE COMMUNICATIONS LETTERS, VOL. 4, NO.5, MAY2000 Effective Forward-Channel Capacity of Non-Dedicated CDPD Networks Apostolis K. Salkintzis, Member, IEEE Abstract—Cellular digital packet data (CDPD) is a mobile packet data technology developed to operate on the spectrum assigned to a telephone cellular network. Since it operates on non-dedicated RF channels, it is subject to channel hopping and its performance is affected by the traffic profile of the underlying telephone system. In this letter, we develop formulas expressing the normalized forward channel capacity in terms of telephone traffic conditions and channel hopping parameters. We show that forward capacity is very near to maximum for telephone network utilization less than one, while it degrades rapidly thereafter. Moreover, we develop an expression for the average hopping rate and we demonstrate the sensitivity of capacity with the number of RF channels. Index Terms—Capacity evaluation, cellular digital packet data, CDPD, mobile data networks, traffic modeling. I. INTRODUCTION C ELLULAR digital packet data (CDPD) [1], [2] is a mobile data technology that permits subordinate packet data oper- ation on the spectrum assigned to a telephone cellular network. It is designed to operate on the idle RF channels of the telephone cellular network, i.e., on non-dedicated RF channels. These idle channels are used to transmit short data messages and establish a packet-switching service. CDPD incorporates mechanisms to find those idle RF channels and mechanisms to hop among them in an attempt to sustain operation under the dynamic traffic con- ditions of the underlying voice network. In this letter, we focus on the forward channel (from base to mobiles) performance of CDPD, and in particular, we study how the telephone traffic characteristics as well as the CDPD channel hopping parameters affect the capacity of this channel. In this original study, which differs from other CDPD studies [3], [4], we also derive several useful mathematical expressions that describe statistically the channel hopping procedure under various operating conditions. II. TELEPHONE NETWORK MODEL For the underlying telephone network, we assume a memory- less M/M/ model, that is, a system with total RF channels, with Poisson phone call arrival rate, and with exponential phone Manuscript received June 8, 1998. The associate editor coordinating the re- view of this letter and approving it for publication was Prof. A. K. Elhakeem. The author was with the Department of Electrical and Computer Engineering, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada. He is now with the Institute for Space Applications and Remote Sensing, National Observatory of Athens, GR-15236, Greece (e-mail: salki@space.noa.gr). Publisher Item Identifier S 1089-7798(00)03845-X. call duration. Under these assumptions the probability to have new phone call arrivals within a time period is given by the Poisson distribution: (1) where is the average phone call arrival rate. Moreover, the probability to find busy channels in the voice system provided that the average call duration is derives directly from Erlang’s formula [5]: (2) III. CHANNEL HOPPING PROCEDURE CDPD transmissions remain on a particular RF channel until either a maximum amount of time elapses, whereupon a planned channel hop occurs, or the current RF channel is acquired by the underlying voice system, whereupon a forced channel hop occurs. In any case, CDPD ceases transmission on the current forward channel and establishes operation on another RF channel, provided there is one available. Just before releasing the current channel and hoping to another, the identity of the new RF channel might be transmitted (if it is already known) in order to assist mobile terminals to track the channel hop as fast as possible [1], [2]. However, when this is not the case, mobile terminals have to hunt around among a designated set of potential RF channels before they find the new CDPD forward channel. IV. ANALYSIS OF EFFECTIVE FORWARD CHANNEL CAPACITY Denoting by the random time period that CDPD dwells on a given RF channel, the probability of a planned channel hop can be written as (3) where is the probability a new phone call to acquire the cur- rently used CDPD channel. By taking into account (1), and as- 1089–7798/00$10.00 © 2000 IEEE