This paper proposes a technique for estimating the computational time of programs in an actor model, which is intended to serve as a compiler target of a wide variety of actor-based programming languages. We define a compositional translation function returning cost equations, which are fed to an automatic off-the-shelf solver for obtaining the time bounds. Our approach is based on a new notion of synchronization sets, which captures possible difficult synchronization patterns between actors and helps make the analysis efficient and precise. The approach is proven to correctly over-approximate the worst computational time of an actor model of concurrent programs. Our technique is complemented by a prototype analyzer that returns upper bound of costs for the actor model.feeding the cost equations produced by a translation function to a off-the-shelf solver, namely the CoFloCo solver [8].However, this technique proposed in [9] has a very severe constraint: invocations were admitted only either on the same actor or on newly created ones, i.e., no invocation on parameters. For instance, according to this constraint, an invocation to a method inner(y, x), where the first parameter is the actor executing the method, cannot occur in the body of a method outer(x, y). The challenge is that, in this case, computing the cost of outer(x, y) requires to know whether there is a synchronization between actors x and y. In case there is, one has to consider that inner(y, x) might be delayed by other methods running on y, which might be independent from outer(x, y).This paper focuses on overcoming this issue. We first compute synchronization sets of actors, which are actors that potentially might interfere with the executions of each other. We then compose the cost of an invocation with the cost of the callee in two ways: (1) it is added, corresponding to sequential compositions, if the arguments of the invocation and those of the caller are in the same synchronization set; (2) it is the maximum value, corresponding to parallel composition, otherwise.We then define a new translation function that takes the synchronization sets of an alt program into account and returns the corresponding set of cost equations.The translation of alt programs into the solver input code [2,8] has been prototyped and can be experimented (see Section 6). This tool, together with the compiler we have defined in [9], allows us to automatically compute the cost of programs in ABS, a prototype language for programming the cloud [13] that is an extension of alt. Experimental results show that our technique is very precise when computing the cost of a number of typical distributed patterns, such as fork-join or map-reduce.Paper overview. The alt language is defined in Section 2 and we discuss in Section 3 the issues in estimating the computational time. Section 4 explains the analysis of computational time by means of a translation function that returns cost equations, and Section 5 discusses the properties of the translation. In Section 6, we illustrate the ...