7.2 The Single Stage Game (SSG) Competition Model

133

7.2The Single Stage Game (SSG) Competition Model

To study the coexistence between competing wireless networks, and specifically overlapping QoS-supporting QBSSs that are coordinated by CCHCs, a competition model approach is taken that is motivated by the theory of games (see Mangold 2000; Mangold et al. 2000; Mangold et al. 2001h; Mangold et al. 2002b). The problem is modeled as a strategic game. A game in a strategic form consists of a finite set of players, a set of actions for each player, a utility function that is common knowledge between the players, and individual requirements per player that parameterize the utility function, to allow the calculation of payoffs for each game stage. Competing CCHCs are modeled as rational players attempting to maximize their payoffs within the game. A payoff is a measurable quantity related to QoS a player observes after playing the game.

In the following, deterministic decision-taking processes are assumed that select a single action out of the set of actions. A single action is also referred to as pure action. Often, game models allow nonsingle, so-called mixed actions to be taken by the decision-taking processes. A player that selects mixed actions relates probabilities to actions instead of selecting one single action. A decision taken by a player in this case is an allocation of a probability to each single action. The reason for the wide use of this type of action is that often games do not converge to stable operation points if mixed actions are not part of the set of actions. This thesis is limited to game models with pure actions, to reflect that the competing CCHCs attempt to guarantee QoS by setting fixed maximum tolerable QoS thresholds. Specifically for the scheduling of isochronous, time-bounded services, or coordinating HiperLAN/2 MAC frames, the points in time when the respective TXOPs start must be accurately defined, only small delays are tolerated. Therefore, in the SSG model of competition, an action taken corresponds to one choice of resource utilization after having some knowledge about the action the opponent player may select.

Sections 7.2.2-7.2.4 describe the details of the SSG, which is the mean to analyze the coexistence of CCHCs.

7.2.1The Superframe as SSG

A CCHC is modeled as player. Within the CCHC protocol stack, the SME includes a decision taking player entity. A CCHC’s utilization of the radio channel is motivated by the requirement of all stations within its QoS supporting BSS, i.e., QBSS. This utilization of the radio channel is attained through selected actions

134 7. The Game Model

and determines the player’s observed payoff. A successfully transmitted beacon marks the begin of each single stage of the game, where a superframe defines the duration of one single stage. Suppose that the beacon is successfully transmitted by one of the competing CCHCs. The length of the superframe, i.e., the period between two subsequent beacons (Superframe Duration, SFDUR), defines the capacity of the radio channel per stage of the game. The requirement for resource

allocations per CCHC i (per player i)			determines the number Li ( n ) , dura-
tions d i	( n ) and starting times t i	( n )	of the TXOPs that players attempt to
1..L	1..L				( n ) . In
allocate. The starting times are determined by the allocation intervals Di
			1..L
these definitions, n is the superframe number and Li the number of				resource

allocations of player i.

Figure 7.1 illustrates an 802.11 superframe that is interpreted as the SSG of two players. Player 1 (CCHC 1) allocates three TXOPs within the nth superframe, and player 2 allocates two TXOPs. Note that in addition to the high priority TXOPs, additional TXOPs may be allocated through EDCF by all contending stations. The duration of those EDCF-TXOPs are limited by the TXOPlimit, which is typically smaller than 1 ms. They are not indicated in the figure.

As already discussed for the interworking approach in Chapter 6, the TXOPs that are considered are the TXOPs that are directly allocated by a CCHC with highest priority, i.e., without collision avoidance. These TXOPs are typically relatively long (2…10 ms) (Mangold et al., 2001d; ETSI, 2000c), and here particularly used to schedule HiperLAN/2 MAC frames, as well as delivering high priority MSDUs. However, there are other TXOPs offering limited QoS support that are allocated in contention under the rules of the EDCF. Those EDCF-TXOPs are not part of the analytical game model that is used to calculate stable operating points (equilibria).

SFDUR(n)[ms]	nth CCHC superframe = the
	nth single-stage game

		D 1(n) [ms]	D 1(n) [ms]			D 1(n) = D		1(n) [ms]
		1	2			L	3
	d	1(n) [ms]	d 1(n) [ms]		d 1(n) [ms]
	1		2			3
								allocated
								by CCHC1
								allocated by
						1...L1		CCHC2
	t 1(n)		t 1(n)	t	1(n)		TXOPs allocated
						by CCHC1 (here, L1=3)
	1		2	3

TBTT	the periodic beacon is successfully		TBTT
		time
	transmitted by one of the CCHCs

Figure 7.1: One superframe is modeled as single shot (i.e., single stage) strategic game of two players (two CCHCs).