Constructions of Optical Priority Queues With Multiple Inputs and Multiple Outputs

In this paper, we consider the constructions of an
N
-to-
K
optical priority queue with buffer Σ
_i=1
^M
d
_i
by using a feedback system consisting of a single (
M
+max[
N
,
K
]) × (
M
+max[
N
,
K
]) (bufferless) optical crossbar switch, min[
N
,
K
] 1× 2 (bufferless) optical crossbar switches, and
M
fiber delay lines with delays
d
₁
,
d
₂
,...,
d
_M
, where N is the number of arrival links and K is the number of departure links of the priority queue. We first obtain two sufficient conditions [the conditions (A1) and (A2) in Section I] for our constructions of
N
-to-
K
optical priority queues. By establishing a space-time advancement property and a monotonically decreasing/increasing property for the packets stored in the fiber delay lines, we then use these sufficient conditions to show that with an appropriate choice for the delays
d
₁
,
d
₂
,...,
d
_M
, we can achieve a buffer size of
O
([(
M
³
/
N
²
)]) for the case that
N
=
K
. For the special case that
N
=
K
=1, our constructions achieve a buffer size of
O
(
M
³
), which is much better than the
O
(
M
²
) buffer size previously known in the literature for single-input single-output optical priority queues. Therefore, other than the extension from the constructions of optical priority queues with a single input and a single output to the constructions of optical priority queues with multiple inputs and multiple outputs, our constructions also achieve a larger buffer size than previous constructions of single-input single-output optical priority queues. Furthermore, we give another sufficient condition [the condition (A3) in Section I] for our constructions of
N
-to-
K
optical priority queues and then use that condition to obtain choices for the delays
d
₁
,
d
₂
,...,
d
_M
so that our constructions have the fault tolerant capability that can tolerate up to
F
broken/malfunctioning fibers (e.g., fiber cut, fiber shorting out, etc.), where 0 ≤
F
≤
M
-1.