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Table 1 Symbols used in this article and their definitions

From: Admission control policy for adaptive multirate multiservices in cellular systems

Symbol

Explanation

M

The set of all cells in a wireless cellular system

A i

The set of cells that are adjacent to cell i

S

The set of multimedia services that are available to mobile users

s

The multimedia services that are available to mobile users

S single - mod e

The set of “single mode services” that are not adaptive-rate services

S full-rate

The set of “dual mode full-rate services” that are adaptive-rate services, but which have not been adapted

S reduced-rate

The set of “dual mode reduced-rate services” that are adaptive-rate services, and which have been adapted

M D C ( s )

A single media stream of the “dual mode full-rate service” that can be cut into two substreams referred to as descriptions (i.e., “dual mode reduced-rate service”)

b s

The basic bandwidth unit (BBU) of each service, s

t s

The connection time, which is the duration of the connection using service type s and an exponentially distributed random variable with mean 1 v s

t s R

The residual (i.e., remaining) connection time, which is exponentially distributed with mean 1 v s

1 / v s

The mean of t s

t b i

The interboundary time, which starts at the moment cell i is entered and that is an exponentially distributed random variable with means 1 η i

1 / η i

The mean of t b i

q i s j s

The probability of attempting a handover of service type s from cell i to neighboring cell j

m i

The occupancy vector for overall services in cell i

m i s '

The number of connections using multimedia service type s ' in cell i

θ i

The set of all feasible m i vectors

λ i s

The arrival rate of the new connection request for service type s in cell i

P i ( m i )

The probability of being in state m i in the |S|-dimensional birth–death process corresponding to cell i

C i

The capacity for cell i

ψ

The threshold of a new connection request

σ

The threshold of a handover request

β n i s ( m i )

The policy of not accepting a new user's connection request for service type s in cell i

β h h i st ( m i )

The policy of not accepting a connection request from a handover user for service type t, which is offered to cell i from service type s in its adjacent cell

B n i s

The probability of blocking connection requests for service type s in cell i of new users

B h h i st

The probability of dropping connection requests for service type t of handover users, which is offered to cell i from service type s in its adjacent cell

h j s i s

The handover rate of service type s, which is offered to cell i from its adjacent cell j

h j s i t

The handover rate of service type t, which is offered to cell i from service type s in its adjacent cell j

The new call arrival rates after processing the CAC policy function

The arrival rates of handover calls that are not adaptive-rate calls after processing the CAC policy function

The arrival rates of handover calls that are adaptive-rate call after processing the CAC policy function