api.aoi

mexify_aoi

@brief MATLAB Coder script to generate MEX functions for aoi_ module.

This script generates MEX (MATLAB Executable) versions of Age of Information (AoI) metric functions for improved performance. Only pure scalar-in/scalar-out functions are included.

Skipped functions (Coder-incompatible):

aoi_lst_det, aoi_lst_exp, aoi_lst_erlang, aoi_lst_ph

Return function handles

aoi_fcfs_mgi1, aoi_fcfs_gim1, aoi_lcfspr_mgi1, aoi_lcfspr_gim1

Take function handle (LST) arguments

aoi_lcfss_mgi1, aoi_lcfss_gim1, aoi_lcfsd_mgi1, aoi_lcfsd_gim1

Take function handle (LST) arguments

aoi_is_aoi - SchedStrategy/NodeType enum dependencies aoi_extract_params - SchedStrategy, sn.proc cell array aoi_dist2ph - Cell array unpacking

See also CODER, CODER.CONFIG, CODER.TYPEOF, CODEGEN.

aoi_lcfspr_mm1(lambda, mu)

AOI_LCFSPR_MM1 Mean, variance, and peak AoI for M/M/1 preemptive LCFS queue

[meanAoI, varAoI, peakAoI] = aoi_lcfspr_mm1(lambda, mu)

Computes the Age of Information metrics for an M/M/1 queue with preemptive Last-Come First-Served (LCFS-PR) discipline.

In LCFS-PR, when a new update arrives, it preempts the current update in service (if any). This ensures the freshest update is always served, leading to lower AoI than FCFS.

Parameters:

lambda (double) – Arrival rate (Poisson arrivals)
mu (double) – Service rate (exponential service)

Returns:

meanAoI (double) – Mean (average) Age of Information varAoI (double): Variance of Age of Information peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Section IV):: Mean AoI: E[A] = (1/mu) * (1 + 1/rho) Peak AoI: E[Apeak] = 1/(lambda+mu) + 1/lambda + 1/mu

Note: LCFS-PR always achieves lower mean AoI than FCFS for M/M/1.

Reference:: Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

See also: aoi_fcfs_mm1(), aoi_lcfspr_mgi1(), aoi_compare

aoi_lcfsd_gim1(Y_lst, mu, E_Y, E_Y2)

AOI_LCFSD_GIM1 Mean AoI for GI/M/1 non-preemptive LCFS-D queue

[meanAoI, lstAoI, peakAoI] = aoi_lcfsd_gim1(Y_lst, mu, E_Y, E_Y2)

Computes the Age of Information metrics for a GI/M/1 queue with non-preemptive Last-Come First-Served with Discarding (LCFS-D) discipline.

In LCFS-D, when a new update arrives while the server is busy:

If there’s an update waiting in queue, it is discarded
The new update takes its place in the queue
When service completes, the waiting update (if any) is served

Parameters:

Y_lst (function_handle) – LST of interarrival time, @(s) -> complex
mu (double) – Service rate (exponential service)
E_Y (double) – Mean interarrival time (first moment)
E_Y2 (double) – Second moment of interarrival time

Returns:

meanAoI (double) – Mean (average) Age of Information lstAoI (function_handle): LST of AoI distribution (empty if not computed) peakAoI (double): Mean Peak Age of Information

Reference:: Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_fcfs_mgi1(lambda, H_lst, E_H, E_H2)

AOI_FCFS_MGI1 Mean AoI and LST for M/GI/1 FCFS queue

[meanAoI, lstAoI, peakAoI] = aoi_fcfs_mgi1(lambda, H_lst, E_H, E_H2)

Computes the Age of Information metrics for an M/GI/1 queue with First-Come First-Served (FCFS) discipline.

M/GI/1: Poisson arrivals with rate lambda, general independent service.

Parameters:

lambda (double) – Arrival rate (Poisson arrivals)
H_lst (function_handle) – LST of service time, @(s) -> complex
E_H (double) – Mean service time (first moment)
E_H2 (double) – Second moment of service time

Returns:

meanAoI (double) – Mean (average) Age of Information lstAoI (function_handle): LST of AoI distribution peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Theorem 2):

LST of AoI: A*(s) = (lambda * H*(s)) / (s + lambda - lambda*H*(s)) * W*(s) where W*(s) is the LST of waiting time (Pollaczek-Khinchine).

Mean AoI (Proposition 1): E[A] = E[H] + E[T] + (1-2*rho)/lambda - d/ds T*(s)|_{s=lambda} (exact)

Reference:

Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_fcfs_gim1(Y_lst, mu, E_Y, E_Y2)

AOI_FCFS_GIM1 Mean AoI and LST for GI/M/1 FCFS queue

[meanAoI, lstAoI, peakAoI] = aoi_fcfs_gim1(Y_lst, mu, E_Y, E_Y2)

Computes the Age of Information metrics for a GI/M/1 queue with First-Come First-Served (FCFS) discipline.

GI/M/1: General independent arrivals, exponential service with rate mu.

Parameters:

Y_lst (function_handle) – LST of interarrival time, @(s) -> complex
mu (double) – Service rate (exponential service)
E_Y (double) – Mean interarrival time (first moment)
E_Y2 (double) – Second moment of interarrival time

Returns:

meanAoI (double) – Mean (average) Age of Information lstAoI (function_handle): LST of AoI distribution peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Theorem 3):

The key parameter sigma is the unique root in (0,1) of:: Y*(mu - mu*sigma) = sigma

LST of AoI: A*(s) = (mu*sigma_s) / (s + mu - mu*sigma_s) * D*(s) where sigma_s solves Y*(s + mu - mu*sigma_s) = sigma_s and D*(s) is the LST of system delay.

Reference:

Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_lcfspr_mgi1(lambda, H_lst, E_H, E_H2)

AOI_LCFSPR_MGI1 Mean AoI and LST for M/GI/1 preemptive LCFS queue

[meanAoI, lstAoI, peakAoI] = aoi_lcfspr_mgi1(lambda, H_lst, E_H, E_H2)

Computes the Age of Information metrics for an M/GI/1 queue with preemptive Last-Come First-Served (LCFS-PR) discipline.

In LCFS-PR, when a new update arrives, it preempts the current update in service (if any). This ensures the freshest update is always served.

Parameters:

lambda (double) – Arrival rate (Poisson arrivals)
H_lst (function_handle) – LST of service time, @(s) -> complex
E_H (double) – Mean service time (first moment)
E_H2 (double) – Second moment of service time (for reference)

Returns:

meanAoI (double) – Mean (average) Age of Information lstAoI (function_handle): LST of AoI distribution peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Section IV):

For preemptive LCFS, the AoI simplifies significantly:: E[A] = E[Y] + E[H] = 1/lambda + E[H] E[Apeak] = -H*(lambda)’/H*(lambda) + 1/(lambda*H*(lambda))

LST of AoI: A*(s) = (lambda/(s+lambda)) * H*(s) This is the convolution of exponential interarrival and service time.

Reference:

Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_lcfspr_gim1(Y_lst, mu, E_Y, E_Y2)

AOI_LCFSPR_GIM1 Mean AoI and LST for GI/M/1 preemptive LCFS queue

[meanAoI, lstAoI, peakAoI] = aoi_lcfspr_gim1(Y_lst, mu, E_Y, E_Y2)

Computes the Age of Information metrics for a GI/M/1 queue with preemptive Last-Come First-Served (LCFS-PR) discipline.

In LCFS-PR, when a new update arrives, it preempts the current update in service (if any). This ensures the freshest update is always served.

Parameters:

Y_lst (function_handle) – LST of interarrival time, @(s) -> complex
mu (double) – Service rate (exponential service)
E_Y (double) – Mean interarrival time (first moment)
E_Y2 (double) – Second moment of interarrival time (for reference)

Returns:

meanAoI (double) – Mean (average) Age of Information lstAoI (function_handle): LST of AoI distribution peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Section IV):

For preemptive LCFS, the AoI simplifies significantly:: E[A] = E[Y] + E[S] = E[Y] + 1/mu E[Apeak] = E[S|success] + 1/(lambda*(1-Y*(mu)))

LST of AoI: A*(s) = Y*(s) * (mu / (s + mu)) This is the product of interarrival LST and exponential service LST.

Reference:

Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_fcfs_dm1(tau, mu)

AOI_FCFS_DM1 Mean, variance, and peak AoI for D/M/1 FCFS queue

[meanAoI, varAoI, peakAoI] = aoi_fcfs_dm1(tau, mu)

Computes the Age of Information metrics for a D/M/1 queue with First-Come First-Served (FCFS) discipline.

D/M/1: Deterministic arrivals with interarrival time tau (rate 1/tau),: exponential service with rate mu.

Parameters:

tau (double) – Deterministic interarrival time
mu (double) – Service rate (exponential service)

Returns:

meanAoI (double) – Mean (average) Age of Information varAoI (double): Variance of Age of Information peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019):

Uses GI/M/1 FCFS results with deterministic arrivals. For D/M/1, the key parameter is sigma, the root of:

sigma = exp(-mu*tau*(1-sigma))

which gives the probability an arriving customer finds system non-empty.

Reference:

Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_lcfss_gim1(Y_lst, mu, E_Y, E_Y2)

AOI_LCFSS_GIM1 Mean AoI for GI/M/1 non-preemptive LCFS-S queue

[meanAoI, lstAoI, peakAoI] = aoi_lcfss_gim1(Y_lst, mu, E_Y, E_Y2)

Computes the Age of Information metrics for a GI/M/1 queue with non-preemptive Last-Come First-Served with Set-aside (LCFS-S) discipline.

In LCFS-S, when a new update arrives while the server is busy:

The new update waits in the queue
When service completes, the most recent update in queue is served next
The older update remains in queue (is “set aside”)

Parameters:

Y_lst (function_handle) – LST of interarrival time, @(s) -> complex
mu (double) – Service rate (exponential service)
E_Y (double) – Mean interarrival time (first moment)
E_Y2 (double) – Second moment of interarrival time

Returns:

meanAoI (double) – Mean (average) Age of Information lstAoI (function_handle): LST of AoI distribution (empty if not computed) peakAoI (double): Mean Peak Age of Information

Reference:: Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_is_aoi(sn)

AOI_IS_AOI Check if network is a valid AoI topology for aoi-fluid analysis

[isAoI, aoiInfo] = AOI_IS_AOI(sn)

Validates that the network structure is suitable for Age of Information analysis using the aoi-fluid MFQ solvers.

Requirements: - Single open class - Single-queue open system: Source -> Queue -> Sink - Queue capacity = 1 (bufferless) or 2 (single-buffer) - Single server (nservers = 1) - Scheduling: FCFS, LCFS, or LCFSPR - For capacity=2: arrivals must be exponential (Poisson)

Parameters:

sn (struct) – Network structure from Network.getStruct()

Returns:

isAoI (logical) – True if topology is valid for AoI analysis aoiInfo (struct): Contains topology information:

.sourceIdx, .queueIdx, .sinkIdx: Node indices .sourceStation, .queueStation: Station indices .capacity: Queue capacity (1 or 2) .schedStrategy: Scheduling strategy .systemType: ‘bufferless’ or ‘singlebuffer’ .errorMsg: Error message if not valid

aoi_extract_params(sn, aoiInfo, options)

AOI_EXTRACT_PARAMS Extract parameters from LINE network for aoi-fluid solvers

[aoiParams, aoiInfo] = AOI_EXTRACT_PARAMS(sn, aoiInfo, options)

Maps LINE model representation to aoi-fluid function inputs: - For bufferless (capacity=1): extract (tau, T, sigma, S, p) - For single-buffer (capacity=2): extract (lambda, sigma, S, r)

Parameters:

sn (struct) – Network structure from Network.getStruct()
aoiInfo (struct) – Topology information from aoi_is_aoi()
options (struct) – Solver options, may contain: - config.aoi_preemption: Override preemption probability (0-1)

Returns:

aoiParams (struct) –

Parameters for aoi-fluid solver:

For bufferless:: .tau: Arrival initial probability vector .T: Arrival sub-generator matrix .sigma: Service initial probability vector .S: Service sub-generator matrix .p: Preemption probability (0=FCFS, 1=preemptive)
For single-buffer:: .lambda: Arrival rate (Poisson) .sigma: Service initial probability vector .S: Service sub-generator matrix .r: Replacement probability (0=FCFS, 1=replacement)

aoiInfo (struct): Updated with extracted parameters

aoi_dist2ph(proc)

AOI_DIST2PH Convert LINE process representation to PH format for aoi-fluid

[alpha, T] = AOI_DIST2PH(proc)

Converts LINE’s {D0, D1} MAP representation to (alpha, T) PH format where alpha is the initial probability vector and T is the sub-generator matrix.

In PH representation:

alpha: Row vector of initial probabilities (sums to 1)
T: Sub-generator matrix (negative diagonal, non-negative off-diagonal)
Absorption rates: -T * ones(n,1)

Parameters:: proc (cell) – LINE process representation {D0, D1} where: D0: Sub-generator matrix (like T in PH) D1: Completion/transition matrix
Returns:: alpha – Initial probability row vector T: Sub-generator matrix

See also: aoi_extract_params(), solveBufferless, solveSingleBuffer

aoi_lcfss_mgi1(lambda, H_lst, E_H, E_H2)

AOI_LCFSS_MGI1 Mean AoI for M/GI/1 non-preemptive LCFS-S queue

[meanAoI, lstAoI, peakAoI] = aoi_lcfss_mgi1(lambda, H_lst, E_H, E_H2)

Computes the Age of Information metrics for an M/GI/1 queue with non-preemptive Last-Come First-Served with Set-aside (LCFS-S) discipline.

In LCFS-S, when a new update arrives while the server is busy:

The new update waits in the queue
When service completes, the most recent update in queue is served next
The older update remains in queue (is “set aside”)

Parameters:

lambda (double) – Arrival rate (Poisson arrivals)
H_lst (function_handle) – LST of service time, @(s) -> complex
E_H (double) – Mean service time (first moment)
E_H2 (double) – Second moment of service time

Returns:

meanAoI (double) – Mean (average) Age of Information lstAoI (function_handle): LST of AoI distribution (empty if not computed) peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Section V):: The analysis is more complex than FCFS or preemptive LCFS. Mean AoI is computed using the results from Theorem 6.
Reference:: Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_lcfsd_mgi1(lambda, H_lst, E_H, E_H2)

AOI_LCFSD_MGI1 Mean AoI for M/GI/1 non-preemptive LCFS-D queue

[meanAoI, lstAoI, peakAoI] = aoi_lcfsd_mgi1(lambda, H_lst, E_H, E_H2)

Computes the Age of Information metrics for an M/GI/1 queue with non-preemptive Last-Come First-Served with Discarding (LCFS-D) discipline.

In LCFS-D, when a new update arrives while the server is busy:

If there’s an update waiting in queue, it is discarded
The new update takes its place in the queue
When service completes, the waiting update (if any) is served

This is also known as M/GI/1/2* (buffer size 2 with replacement).

Parameters:

lambda (double) – Arrival rate (Poisson arrivals)
H_lst (function_handle) – LST of service time, @(s) -> complex
E_H (double) – Mean service time (first moment)
E_H2 (double) – Second moment of service time

Returns:

meanAoI (double) – Mean (average) Age of Information lstAoI (function_handle): LST of AoI distribution (empty if not computed) peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Section VI):: The analysis uses the concept of effective service time which includes potential waiting while another update is being served.
Reference:: Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_fcfs_mm1(lambda, mu)

AOI_FCFS_MM1 Mean, variance, and peak AoI for M/M/1 FCFS queue

[meanAoI, varAoI, peakAoI] = aoi_fcfs_mm1(lambda, mu)

Computes the Age of Information metrics for an M/M/1 queue with First-Come First-Served (FCFS) discipline.

Parameters:

lambda (double) – Arrival rate (Poisson arrivals)
mu (double) – Service rate (exponential service)

Returns:

meanAoI (double) – Mean (average) Age of Information varAoI (double): Variance of Age of Information peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019):: Mean AoI: E[A] = (1/mu) * (1 + 1/rho + rho^2/(1-rho)) Peak AoI: E[Apeak] = (1/mu) * (1 + 1/rho + rho/(1-rho))
Reference:: Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

See also: aoi_lcfspr_mm1(), aoi_fcfs_mgi1(), aoi_optimal_rate

aoi_fcfs_md1(lambda, d)

AOI_FCFS_MD1 Mean, variance, and peak AoI for M/D/1 FCFS queue

[meanAoI, varAoI, peakAoI] = aoi_fcfs_md1(lambda, d)

Computes the Age of Information metrics for an M/D/1 queue with First-Come First-Served (FCFS) discipline.

M/D/1: Poisson arrivals with rate lambda, deterministic service time d.

Parameters:

lambda (double) – Arrival rate (Poisson arrivals)
d (double) – Deterministic service time

Returns:

meanAoI (double) – Mean (average) Age of Information varAoI (double): Variance of Age of Information peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019):: Uses M/GI/1 FCFS results with deterministic service. For M/D/1:

E[H] = d, E[H^2] = d^2 (deterministic) rho = lambda * d E[W] = lambda * d^2 / (2*(1-rho)) (Pollaczek-Khinchine) E[T] = E[W] + d E[A] = d*(1/2 + 1/(2*(1-rho)) + ((1-rho)/rho)*exp(rho)) (exact)
Reference:: Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_lcfspr_md1(lambda, d)

AOI_LCFSPR_MD1 Mean, variance, and peak AoI for M/D/1 preemptive LCFS queue

[meanAoI, varAoI, peakAoI] = aoi_lcfspr_md1(lambda, d)

Computes the Age of Information metrics for an M/D/1 queue with preemptive Last-Come First-Served (LCFS-PR) discipline.

In LCFS-PR, when a new update arrives, it preempts the current update in service (if any). For M/D/1, an update is successful if no new arrivals occur during its deterministic service time d.

Parameters:

lambda (double) – Arrival rate (Poisson arrivals)
d (double) – Deterministic service time

Returns:

meanAoI (double) – Mean (average) Age of Information varAoI (double): Variance of Age of Information peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Section IV):

For preemptive LCFS with M/G/1:: E[A] = E[Y] + E[S] = 1/lambda + d

where S is the (successful) service time, which equals d.

Reference:

Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_lcfspr_dm1(tau, mu)

AOI_LCFSPR_DM1 Mean, variance, and peak AoI for D/M/1 preemptive LCFS queue

[meanAoI, varAoI, peakAoI] = aoi_lcfspr_dm1(tau, mu)

Computes the Age of Information metrics for a D/M/1 queue with preemptive Last-Come First-Served (LCFS-PR) discipline.

In LCFS-PR, when a new update arrives, it preempts the current update in service (if any). For D/M/1, arrivals are deterministic (every tau time units) and service is exponential with rate mu.

Parameters:

tau (double) – Deterministic interarrival time
mu (double) – Service rate (exponential service)

Returns:

meanAoI (double) – Mean (average) Age of Information varAoI (double): Variance of Age of Information peakAoI (double): Mean Peak Age of Information

Formulas (from Inoue et al., IEEE Trans. IT, 2019, Section IV):

For preemptive LCFS with GI/M/1:: E[A] = E[Y] + E[S] = tau + 1/mu

where S is the service time (exponential).

Reference:

Y. Inoue, H. Masuyama, T. Takine, T. Tanaka, “A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues,” IEEE Trans. Information Theory, vol. 65, no. 12, pp. 8305-8324, 2019.

aoi_lst_ph(alpha, T)

AOI_LST_PH Laplace-Stieltjes transform for phase-type distribution

lst = aoi_lst_ph(alpha, T)

Returns a function handle for the LST of a phase-type (PH) distribution with initial probability vector alpha and sub-generator matrix T.

Parameters:

alpha (row vector) – Initial probability vector (1 x n)
T (matrix) – Sub-generator matrix (n x n)

Returns:

lst (function_handle) – LST function @(s) alpha * inv(s*I - T) * (-T*e)

The LST of PH(alpha, T) is: H*(s) = alpha * (s*I - T)^{-1} * t where t = -T * ones(n,1) is the exit rate vector.

For numerical stability, we use: H*(s) = alpha * ((s*I - T) t)

aoi_lst_exp(mu)

AOI_LST_EXP Laplace-Stieltjes transform for exponential distribution

lst = aoi_lst_exp(mu)

Returns a function handle for the LST of an exponential distribution with rate mu.

Parameters:: mu (double) – Rate parameter (mean = 1/mu)
Returns:: lst (function_handle) – LST function @(s) mu/(mu+s)

The LST of Exp(mu) is: H*(s) = mu / (mu + s)

aoi_lst_erlang(k, mu)

AOI_LST_ERLANG Laplace-Stieltjes transform for Erlang distribution

lst = aoi_lst_erlang(k, mu)

Returns a function handle for the LST of an Erlang-k distribution with rate parameter mu.

Parameters:

k (integer) – Shape parameter (number of phases)
mu (double) – Rate parameter per phase (mean = k/mu)

Returns:

lst (function_handle) – LST function @(s) (mu/(mu+s))^k

The LST of Erlang(k, mu) is: H*(s) = (mu / (mu + s))^k

aoi_lst_det(d)

AOI_LST_DET Laplace-Stieltjes transform for deterministic (constant) distribution

lst = aoi_lst_det(d)

Returns a function handle for the LST of a deterministic distribution with constant value d.

Parameters:: d (double) – Constant value (must be positive)
Returns:: lst (function_handle) – LST function @(s) exp(-s*d)

The LST of a deterministic random variable X = d is: H*(s) = exp(-s*d)