10 distance of the users from their serving BSs remain nearly the same, however, the small scale fading gain on the considered subcarrier may vary from one time slot to the other. We select the user with maximum SNR in each time slot T$_{w}$ , however once a user is selected from a ring, all users located in that ring will not be scheduled for transmission for the next K − 1 time slots. Note that all BSs are considered to be time synchronized in terms of scheduling. Clearly, the probability of allocating a ring k at T$_{1}$ can simply be given by (11). However, the probability of selecting a ring k at T$_{2}$ is a dependent event and can be derived using Bayes theorem as follows: where, P ( r$_{sel}$ = r T 2 k ) = K ∑ j =1 j = k P ( r$_{sel}$ = r$_{k}$ T 2 r$_{sel}$ = r$_{j}$ T 1 ) P ( r$_{sel}$ = r T 1 j ) (18) P ( r$_{sel}$ = r$_{k}$ T 2 r$_{sel}$ = r$_{j}$ T 1 ) = ∫ ∞ 0 K ∏ i = k i = j ( F$_{ζ}$ ( γ$_{k}$r β $_{i}$) ) u$_{i}$ u$_{k}$f$_{ζ}$ ( γ$_{k}$r β $_{k}$) r − β k ( F$_{ζ}$ ( γ$_{k}$r β $_{k}$) ) u$_{k}$ − $^{1}$dγ$_{k}$ (19) Since the probability of allocating any ring k within time slot T$_{w}$ depends on all previous states, therefore, the principle of Markov chain transition probabilities is not directly applicable. For more clarity, the probability of selecting a ring k at T$_{3}$ is given as follows: P ( r$_{sel}$ = r T 3 k ) = K ∑ m = k K ∑ j = m j = k P ( r$_{sel}$ = r$_{k}$ T 3 r$_{sel}$ = r$_{j}$ T 2 ∩ r$_{sel}$ = r$_{m}$ T 1 ) P ( r$_{sel}$ = r$_{j}$ T 2 r$_{sel}$ = r$_{m}$ T 1 ) P ( r$_{sel}$ = r T 1 $_{m}$) (20) P ( r$_{sel}$ = r$_{k}$ T 3 r$_{sel}$ = r$_{j}$ T 2 ∩ r$_{sel}$ = r$_{m}$ T 1 ) = ∫ ∞ 0 K ∏ i = k i = j,i = $_{m}$( F$_{ζ}$ ( γ$_{k}$r β $_{i}$) ) u$_{i}$ u$_{k}$f$_{ζ}$ ( γ$_{k}$r β $_{k}$) r − β k ( F$_{ζ}$ ( γ$_{k}$r β $_{k}$) ) u$_{k}$ − $^{1}$dγ$_{k}$ (21) Computational Efficiency: The time complexity of the greedy round robin scheme is heavily based on the computational time of the NIntegrate operation in MATHEMATICA . One NIntegrate operation requires around 0.95 sec which is equivalent to the computational complexity of (i) greedy scheme and K ∑ n = k K ∑ s = n, s = k · · · ∑ j = s,n,.. j = k P ( r$_{sel}$ = r$_{k}$ T$_{w}$ r$_{sel}$ = r$_{j}$ T$_{w}$$_{−}$ 1 · · · ∩ r$_{sel}$ = r$_{s}$ T 2 ∩ r$_{sel}$ = r$_{n}$ T 1 ) · · · P ( r$_{sel}$ = r$_{s}$ T 2 r$_{sel}$ = r$_{n}$ T 1 ) P ( r$_{sel}$ = r T 1 n ) (22) In general, the probability of selecting any ring k at a time slot T$_{w}$ , i.e., P ( r$_{sel}$ = r T$_{w}$ k ) can be written as: where,