Comparing approximations in the ASIP tandem queue

Tandem stochastic systems (TSSs) are networks of simple stochastic components through which particles—customers, jobs, molecules—move sequentially. Despite the apparent simplicity of individual nodes, their aggregate dynamics are often highly complex. TSSs are widely used in communication networks [2], operations research [3], and physics [7]. The Asymmetric Inclusion Process (ASIP) [5] differs by allowing clustering: multiple particles may occupy the same site forming inseparable clusters that move together. It thus models unidirectional transport with irreversible aggregation, bridging TJNs and ASEP. ASIP captures clustering phenomena observed in road traffic [9], maritime logistics [6], and intracellular transport [4]. However, unlike TJNs, ASIP lacks product-form solutions; its state-space dependencies make exact stationary distributions intractable beyond very small systems. Existing attempts [10] show that the number of equations grows exponentially with sites, and only asymptotic approximations are available. This motivates the search for tractable approximations.